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Related problems of cut locus and a generalization of Jacobi's last theorem

Research Project

Project/Area Number 20540085
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionKumamoto University

Principal Investigator

ITOH Jin-ichi  Kumamoto University, 教育学部, 教授 (20193493)

Co-Investigator(Kenkyū-buntansha) KIYOHARA Kazuyoshi  岡山大学, 理学部, 教授 (80153245)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords幾何学 / 測地線 / 最小跡 / 共役跡 / 第1共役跡 / グラフ / 多面体の折り畳み / 多面体の展開 / Liouviile多様体 / Parallelohedra / 単純閉測地線 / 2次曲面 / Liouville多様体 / 距離関数 / 単純閉擬測地線 / Liouville 多様体 / 鋭角三角形分割
Research Abstract

The cut locus of an ellipsoid is an arc on the elliptic coordinate, and the conjugate locus has exactly 4 cusps which is known as Jacobi's last theorem. In this study we determined the cut locus on a general dimensional ellipsoid, and determined the structure of conjugate locus and its singularities. Moreover we studied cut loci of some kind of Liouville manifolds and the relations of cut locus of general surfaces and graphs.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (105 results)

All 2011 2010 2009 2008 Other

All Journal Article (46 results) (of which Peer Reviewed: 39 results) Presentation (59 results)

  • [Journal Article] On Liouville integrability of h-projectively equivalent Kaehler metrics2011

    • Author(s)
      K.Kiyohara, P.Topalov
    • Journal Title

      Proc.Amer.Math.Soc. 139

      Pages: 231-242

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The cut loci on ellipsoids and certain Liouville manifolds2010

    • Author(s)
      J.Itoh, K.Kiyohara
    • Journal Title

      Asian J.Math. 14

      Pages: 257-289

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Star unfolding convex polyhedra via quasigeodesic loops.2010

    • Author(s)
      J.Itoh, J.O'Rourke, C.Vilcu
    • Journal Title

      Discrete Comp.Geom. 44

      Pages: 35-54

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Gauss-Bonnet type formula on Riemann-Finsler surfaces with nonconstant indicatorix volume.2010

    • Author(s)
      J.Itoh, S.V.Sabau, H.Shimada
    • Journal Title

      Kyoto J.Math. 50

      Pages: 165-195

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Reflective space-filling polyhedra.2010

    • Author(s)
      J.Itoh, C.Nara
    • Journal Title

      Int.J.Pure Appl.Math. 58

      Pages: 87-98

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Hermite-Liouville manifolds2010

    • Author(s)
      M.Igarashi, K.Kiyohara
    • Journal Title

      J.Math.Soc.Japan 62

      Pages: 895-933

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The cut loci on ellipsoids and certain Liouville manifolds2010

    • Author(s)
      J.Itoh, K.Kiyohara
    • Journal Title

      Asian J.Math.

      Volume: 14 Pages: 257-289

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Chie Minimal surface area related to Kelvin's conjecture2010

    • Author(s)
      J.Itoh, C.Nara
    • Journal Title

      Kumamoto J.Math.

      Volume: 23 Pages: 49-61

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Star unfolding convex polyhedra via quasigeodesic loops2010

    • Author(s)
      J.Itoh, J.O'Rourke, C.Vilcu
    • Journal Title

      Discrete Comput.Geom.

      Volume: 44 Pages: 35-54

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Gauss-Bonnet-type formula on Riemann-Finsler surfaces with nonconstant indicatrix volume2010

    • Author(s)
      Itoh, J. ; Sabau, S.V. ; Shimada, H.
    • Journal Title

      Kyoto J.Math.

      Volume: 50 Pages: 165-192

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 三角形と円から決まる点についての研究2010

    • Author(s)
      伊藤仁一, Jamsran Buyant
    • Journal Title

      熊本大学教育学部紀要 自然科学

      Volume: 59 Pages: 11-18

    • Related Report
      2010 Annual Research Report
  • [Journal Article] 教育学研究科における数学の研究-修士論文指導等における2,3の事例-2010

    • Author(s)
      伊藤仁一
    • Journal Title

      数理解析研究所講究録

      Volume: 1711 Pages: 204-209

    • Related Report
      2010 Annual Research Report
  • [Journal Article] 「教員養成大学・学部の数学専門科目の講義内容についての調査」の結果とその考察2010

    • Author(s)
      丹羽, 松岡, 川崎, 伊藤
    • Journal Title

      数理解析研究所講究録

      Volume: 1711 Pages: 89-105

    • Related Report
      2010 Annual Research Report
  • [Journal Article] 中学校・高等学校の数学教師の養成における数学専門科目の標準的なモデルの構想2010

    • Author(s)
      丹羽, 松岡, 川崎, 大竹, 伊藤
    • Journal Title

      数理解析研究所講究録

      Volume: 1711 Pages: 106-129

    • Related Report
      2010 Annual Research Report
  • [Journal Article] On Hermite-Liouville manifolds2010

    • Author(s)
      M.Igarashi, K.Kiyohara
    • Journal Title

      J.Math.Soc.Japan

      Volume: 62 Pages: 895-933

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Space-filling polyhedra with reflectiveness2010

    • Author(s)
      J.Itoh, C.Nara
    • Journal Title

      Int.J.Pure Appl.Math. 58

      Pages: 87-98

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] ダイヤモンドと正多面体2010

    • Author(s)
      奈良知恵, 伊藤仁一
    • Journal Title

      数学モミナー 49

      Pages: 45-49

    • Related Report
      2009 Annual Research Report
  • [Journal Article] What do cylinder look like?2009

    • Author(s)
      J.Itoh, C.Vilcu
    • Journal Title

      J.Geom. 95

      Pages: 41-48

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Criteria for farthest points on convex surface.2009

    • Author(s)
      J.Itoh, C.Vilcu
    • Journal Title

      Math.Nachr. 282

      Pages: 1537-1547

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Some remarks on simple closed geodesics with ends.2009

    • Author(s)
      J.Itoh, F.Ohtsuka, T.Zamfirescu
    • Journal Title

      Bull.Math.Soc.Sci.Math.Roumanie 52

      Pages: 311-319

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Acute triangulations of flat tori.2009

    • Author(s)
      J.Itoh, L.Yuan
    • Journal Title

      Europian J.Combin. 30

      Pages: 1-4

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Criteria for farthest points on convex surfaces2009

    • Author(s)
      J.Itoh, C.Vilcu
    • Journal Title

      Math.Nachrichten 282

      Pages: 1-11

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some remarks on simple closed geodesics of surfaces with ends2009

    • Author(s)
      J.Itoh, F.Ohtsuka, T.Zamfirescu
    • Journal Title

      Bull.Math.Soc.Roumanie 52

      Pages: 311-319

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] What do cylinders look like?2009

    • Author(s)
      J.Itoh, C.Vilcu
    • Journal Title

      J.of Geometry 95

      Pages: 41-48

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 教育学研究科における数学の研究-直観幾何学的視点から-2009

    • Author(s)
      伊藤仁一
    • Journal Title

      数理解析研究所講究録 1657

      Pages: 157-176

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Acute triangulations of flat tori2009

    • Author(s)
      J. Itoh &L. Yuan
    • Journal Title

      European J. Combin. 30

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The total absolute curvature of open curves in E3.2008

    • Author(s)
      K.Enomoto, J.Itoh, R.Sinclair
    • Journal Title

      Illinois J.Math. 52

      Pages: 47-76

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Antipodal convex hypersurfaces.2008

    • Author(s)
      J.Itoh, J.Rouyer, C.Vilcu
    • Journal Title

      Indag.Math. 19

      Pages: 411-426

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On triangulations of the surface of a cube into planar acute triangles.2008

    • Author(s)
      J.Itoh, H.Maehara
    • Journal Title

      Ryukyu Math.J. 21

      Pages: 15-22

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On triangulations of the surface of a cube into planar acute triangles2008

    • Author(s)
      J. Itoh &H. Maehara
    • Journal Title

      Eyukyu Math. J. 21

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The total absolute curvature of open curves in $E^3$2008

    • Author(s)
      K. Enomoto J. Itoh & R. Sinclair
    • Journal Title

      Illinois J. of Math. (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cut Loci and conjugate loci on Liouville surfaces

    • Author(s)
      J.Itoh, K.Kiyohara
    • Journal Title

      manuscripta math. (to appear)受理済

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Unfoldings of doubly covered polyhedra and applications to space-fillers

    • Author(s)
      J.Itoh, C.Nara
    • Journal Title

      Periodica Math.Hungarica (to appear)受理済

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Quasigeodesics and farthest points on convex surfaces

    • Author(s)
      K.Ieiri, J.Itoh, C.Vilcu
    • Journal Title

      Advances in Geometry (to appear)受理済

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Moderation of convex bodies

    • Author(s)
      J.Itoh, T.Zamfirescu
    • Journal Title

      J.of Convex Analysis

      Volume: (発表受理)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cut Loci and conjugate loci on Liouville surfaces

    • Author(s)
      J.Itoh, K.Kiyohara
    • Journal Title

      manuscripta math.

      Volume: (発表受理)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Unfoldings of doubly covered polyhedra and applications to space-fillers

    • Author(s)
      Jin-ichi Itoh, Chie Nara
    • Journal Title

      Periodica Math.Hungarica

      Volume: (発表受理)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cut locus structures on graphs

    • Author(s)
      Jin-ichi Itoh, Costin Vilcu
    • Journal Title

      Discrete Mathematics

      Volume: (発表受理)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Liouville integrability of h-projectively equivalent Kahler metrics

    • Author(s)
      K.Kiyohara, P.Topalov
    • Journal Title

      Proc.of Amer.Math.Soc.

      Volume: (発表受理)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Star unfolding convex polyhedra via quasigeodesics

    • Author(s)
      J.Itoh, J.O'Rourke, C.Vilcu
    • Journal Title

      Discrete Comput.Geometry (掲載確定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Gauss-Bonnet type formula on Riemann-Finsler surfaces with non-constant indicatrix volume

    • Author(s)
      J.Itoh, S.Sabau, H.Shimada
    • Journal Title

      Kyoto J.of Math. (掲載確定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Cut Loci on Ellipsoids and Certain Liouville Manifolds

    • Author(s)
      J.Itoh, K.Kiyohara
    • Journal Title

      The Asian Journal of Mathematics (掲載確定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Minimal surface area related to Kelvin's conjecture

    • Author(s)
      J.Itoh, C.Nara
    • Journal Title

      Kumamoto Math.J. (掲載確定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Antipodal convex hypersurfaces

    • Author(s)
      J. Itoh J. Rouyer & C. Vilcu
    • Journal Title

      Indagationes Math. (発表受理)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Criteria for farthest points on convex surfaces

    • Author(s)
      J. Itoh C. Vilcu
    • Journal Title

      Math. Nachrichten (発表受理)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some remarks on simple closed geodesies of surfaces with ends

    • Author(s)
      J. Itoh F. Ohtsuka, T. Zamfirescu
    • Journal Title

      Bull. Math. Soc. Roumanie (発表受理)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Moderation on convex bodies2011

    • Author(s)
      伊藤仁一
    • Organizer
      日本数学会年会幾何学分科会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-03-22
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 正多面体の連続的折りたたみによる平面化2011

    • Author(s)
      奈良知恵
    • Organizer
      日本数学会年会応用数学分科会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-03-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] Moderation on convex bodies2011

    • Author(s)
      伊藤仁一
    • Organizer
      多様体上の種々の幾何構造とその応用
    • Place of Presentation
      名城大学
    • Year and Date
      2011-03-09
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 教育学研究科における研究課題--直観幾何学的視点とその事例--2011

    • Author(s)
      伊藤仁一
    • Organizer
      数学リテラシーを育成する数学教員養成カリキュラムの研究
    • Place of Presentation
      南九州大学
    • Year and Date
      2011-02-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] 正多面体を折り畳む2011

    • Author(s)
      奈良知恵
    • Organizer
      研究会「直観幾何学」
    • Place of Presentation
      熊本大学
    • Year and Date
      2011-02-11
    • Related Report
      2010 Annual Research Report
  • [Presentation] 三角形と円から決まる点についての研究2011

    • Author(s)
      Jamsran Buyant
    • Organizer
      測地線および関連する諸問題
    • Place of Presentation
      熊本大学
    • Year and Date
      2011-01-09
    • Related Report
      2010 Annual Research Report
  • [Presentation] 年多面体を折り畳む2010

    • Author(s)
      奈良知恵
    • Organizer
      第9回折り紙の科学・数学・教育研究集会
    • Place of Presentation
      JOASホール(東京)
    • Year and Date
      2010-12-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] 最小面積の境界をもつ3次元空間分割とケルヴィン予想2010

    • Author(s)
      奈良知恵
    • Organizer
      第4回組合せ数学セミチー
    • Place of Presentation
      九州大学
    • Year and Date
      2010-11-20
    • Related Report
      2010 Annual Research Report
  • [Presentation] Continuous flattening Platonic polyhedral The China-Japan joint conf.on Computation Geometry2010

    • Author(s)
      伊藤仁一
    • Organizer
      Graphs and Applications
    • Place of Presentation
      Dalian Maritime Univ.(Dalian, China)
    • Year and Date
      2010-11-04
    • Related Report
      2010 Final Research Report
  • [Presentation] Continuous flattening Platonic polyhedra2010

    • Author(s)
      J.Itoh
    • Organizer
      The China-Japan joint conf.on Computation Geometry, Graphs and Applications
    • Place of Presentation
      Dalian Maritime Univ.(Dalian, China)
    • Year and Date
      2010-11-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] Affine equivalence classes of parallelohedra2010

    • Author(s)
      C.Nara
    • Organizer
      The China-Japan joint conf.on Computation Geometry, Graphs and Applications
    • Place of Presentation
      Dalian Maritime Univ.(Dalian, China)
    • Year and Date
      2010-11-03
    • Related Report
      2010 Annual Research Report
  • [Presentation] Moderation on convex bodies2010

    • Author(s)
      伊藤仁一
    • Organizer
      幾何学研究会
    • Place of Presentation
      福岡大学セミナーハウス
    • Year and Date
      2010-10-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] The cut locus and the related topics Geometry seminar2010

    • Author(s)
      伊藤仁一
    • Place of Presentation
      Leipzig Univ.(Leipzig, Germany)
    • Year and Date
      2010-09-30
    • Related Report
      2010 Final Research Report
  • [Presentation] The cut locus and the related topics2010

    • Author(s)
      J.Itoh
    • Organizer
      Geometry seminar
    • Place of Presentation
      Leipzig Univ.(Leipzig, Germany)
    • Year and Date
      2010-09-30
    • Related Report
      2010 Annual Research Report
  • [Presentation] 2次元正定曲率正則多面体の分類2010

    • Author(s)
      大塚富美子
    • Organizer
      日本数学会秋季総合分科会幾何学分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] The cut locus, the conjugate locus and related topics2010

    • Author(s)
      伊藤仁一
    • Organizer
      Geometry seminar
    • Place of Presentation
      Stuttgart Univ.(Stuttgart, Germany)
    • Year and Date
      2010-09-22
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Parallelohedraのアフィン同値クラスの表現2010

    • Author(s)
      奈良知恵
    • Organizer
      日本数学会秋季総合分科会応用数学分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] Cut locus structures on graphs, Differential Geometry and its Applications2010

    • Author(s)
      伊藤仁一
    • Place of Presentation
      Masaryk Univ.(Brno, Czech)
    • Year and Date
      2010-08-30
    • Related Report
      2010 Final Research Report
  • [Presentation] Cut locus structures on graphs2010

    • Author(s)
      J.Itoh
    • Organizer
      Differential Geometry and its Applications 2010
    • Place of Presentation
      Masaryk Univ.(Brno, Czech)
    • Year and Date
      2010-08-30
    • Related Report
      2010 Annual Research Report
  • [Presentation] Singular semi-classical approximation on Liouville surfaces2010

    • Author(s)
      K.Kiyohara
    • Organizer
      Differential Geometry and its Applications 2010
    • Place of Presentation
      Masaryk Univ.(Brno, Czech)
    • Year and Date
      2010-08-30
    • Related Report
      2010 Annual Research Report
  • [Presentation] The cut loci and the conjugate loci on n-dim.Ellipsoids, Geometry, Topology2010

    • Author(s)
      伊藤仁一
    • Organizer
      Algebra and Number Theory, Applications (Delone 120)
    • Place of Presentation
      Steklov Math.Inst.(Moscow, Russia)
    • Year and Date
      2010-08-19
    • Related Report
      2010 Final Research Report
  • [Presentation] The cut loci and the conjugate loci on n-dim.ellipsoids2010

    • Author(s)
      J.Itoh
    • Organizer
      Geometry, Topology, Algebra and Number Theory, Applications (Delone 120)
    • Place of Presentation
      Steklov Math.Inst.(Moscow, Russia)
    • Year and Date
      2010-08-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Unfoldings of doubly covered polyhedra and space-fillers with minimum surface area2010

    • Author(s)
      C.Nara
    • Organizer
      Geometry, Topology, Algebra and Number Theory, Applications (Delone 120)
    • Place of Presentation
      Steklov Math.Inst.(Moscow, Russia)
    • Year and Date
      2010-08-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Cut locus structures on graphs, Combinatorics 20102010

    • Author(s)
      伊藤仁一
    • Place of Presentation
      Hotel Il Chiostro (Verbania, Italy)
    • Year and Date
      2010-07-02
    • Related Report
      2010 Final Research Report
  • [Presentation] Cut locus structures on graphs2010

    • Author(s)
      J.Itoh
    • Organizer
      Combinatorics 2010
    • Place of Presentation
      Hotel Il Chiostro (Verbania, Italy)
    • Year and Date
      2010-07-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] Parallelohedraのアフィン同値なクラスについて2010

    • Author(s)
      奈良知恵
    • Organizer
      小研究会「有限幾何とその周辺」
    • Place of Presentation
      熊本大学
    • Year and Date
      2010-05-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] What do cylinders look like ?2010

    • Author(s)
      伊藤仁一
    • Organizer
      日本数学会年会幾何学分科会
    • Place of Presentation
      慶応大学
    • Year and Date
      2010-03-26
    • Related Report
      2010 Final Research Report
  • [Presentation] What do cylinders look like2010

    • Author(s)
      伊藤仁一
    • Organizer
      日本数学会年会幾何学分科会
    • Place of Presentation
      慶応大学
    • Year and Date
      2010-03-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Several topics of intuitive geometry2010

    • Author(s)
      伊藤仁一
    • Organizer
      多様体上の種々の幾何構造とその応用
    • Place of Presentation
      名城大学
    • Year and Date
      2010-03-09
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] Some topics of intuitive geometry2010

    • Author(s)
      伊藤仁一
    • Organizer
      研究会「直観幾何学」
    • Place of Presentation
      熊本大学
    • Year and Date
      2010-02-14
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] ケルビンの問題と切頭八面体2010

    • Author(s)
      奈良知恵
    • Organizer
      研究会「直観幾何学」
    • Place of Presentation
      熊本大学
    • Year and Date
      2010-02-13
    • Related Report
      2009 Annual Research Report
  • [Presentation] 多角形や多面体上のビリヤード軌道とそのブロッキングポイント2010

    • Author(s)
      吉里泰志
    • Organizer
      測地線および関連する諸問題
    • Place of Presentation
      熊本大学
    • Year and Date
      2010-01-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] Closed geodesics on regular dodecahedron2010

    • Author(s)
      田上雄一
    • Organizer
      測地線および関連する諸問題
    • Place of Presentation
      熊本大学
    • Year and Date
      2010-01-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] 教育学研究科における研究・のあり方について2009

    • Author(s)
      伊藤仁一
    • Organizer
      数学リテラシーを育てるための数学教員養成カリキュラム
    • Place of Presentation
      南九州大学
    • Year and Date
      2009-12-16
    • Related Report
      2009 Annual Research Report
  • [Presentation] 4次元単体の最小表面積の展開図について2009

    • Author(s)
      奈良知恵
    • Organizer
      第21回位相幾何学的グラフ理論研究集会
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2009-11-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Minimal surface area of polyhedral unfoldings, Japan conf.on Comput.2009

    • Author(s)
      C.Nara
    • Organizer
      Geometry and Graphs
    • Place of Presentation
      Kanazawa Culture Hall
    • Year and Date
      2009-11-13
    • Related Report
      2010 Final Research Report
  • [Presentation] Minimal surface area of polyhedral unfoldings2009

    • Author(s)
      奈良知恵
    • Organizer
      Japan conf. on Comput. Geometry and Graphs
    • Place of Presentation
      Kanazawa Culture Hall
    • Year and Date
      2009-11-13
    • Related Report
      2009 Annual Research Report
  • [Presentation] 曲面上の閉測地線の数について2009

    • Author(s)
      大塚富美子
    • Organizer
      日本数学会秋季総合分科会幾何学分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] 最小表面積をもつ多面体的展開図について2009

    • Author(s)
      奈良知恵
    • Organizer
      日本数学会秋季総合分科会応用数学分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-27
    • Related Report
      2009 Annual Research Report
  • [Presentation] 最小跡及び関連する諸問題2009

    • Author(s)
      伊藤仁一
    • Organizer
      東海大学・幾何セミナー―田中實先生還暦祝い―
    • Place of Presentation
      東海大学理学部
    • Year and Date
      2009-09-21
    • Related Report
      2009 Annual Research Report
  • [Presentation] 最小表面積をもつ多面体的展開図2009

    • Author(s)
      奈良知恵
    • Organizer
      離散数学とその応用研究集会2009
    • Place of Presentation
      茨城大学
    • Year and Date
      2009-08-23
    • Related Report
      2009 Annual Research Report
  • [Presentation] The cut loci and conjugate loci on ellipsoids2009

    • Author(s)
      伊藤仁一
    • Organizer
      11th International Conference on Discrete Mathematics : Convexity and Discrete Geometry
    • Place of Presentation
      Dortmund Univ.
    • Year and Date
      2009-07-27
    • Related Report
      2010 Final Research Report
  • [Presentation] The cut loci and conjugate loci on ellipsoids2009

    • Author(s)
      伊藤仁一
    • Organizer
      11th International Conference on Discrete Mathematics : Convexity and Discrete Geometry
    • Place of Presentation
      Dortmund Univ
    • Year and Date
      2009-07-27
    • Related Report
      2009 Annual Research Report
  • [Presentation] リーマン多様体の最小跡と関連する諸問題2009

    • Author(s)
      J.Itoh
    • Organizer
      奈良女子大学数学教室談話会
    • Place of Presentation
      奈良女子大学
    • Year and Date
      2009-06-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] 教育系修士課程の修士論文について-具体的指導の例示-2009

    • Author(s)
      伊藤仁一
    • Organizer
      日本数学会教育委員会主催教育シンポジュウム
    • Place of Presentation
      東京大学駒場キャンパス
    • Year and Date
      2009-03-29
    • Related Report
      2010 Final Research Report
  • [Presentation] 教育系修士課程の修士論文について--具体的指導の例示--2009

    • Author(s)
      伊藤 仁一
    • Organizer
      日本数学会教育委員会主催教育シンポジュウム
    • Place of Presentation
      東京大学駒場キャンパス
    • Year and Date
      2009-03-29
    • Related Report
      2008 Annual Research Report
  • [Presentation] Acute triangulations of flat tori2009

    • Author(s)
      伊藤仁一
    • Organizer
      日本数学会年会幾何学分科会
    • Place of Presentation
      東京大学駒場キャンパス
    • Year and Date
      2009-03-27
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] Source Unfoldings of Convex Polyhedra with respect to Certain Closed Polygonal Curves2009

    • Author(s)
      J.O'Rourke
    • Organizer
      25th Europian Workshop on Computational Geometry
    • Place of Presentation
      Brussels (Belgium)
    • Year and Date
      2009-03-16
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] Unfolding convex polyhedra via quasigeodesic sourcw & star unfoldings2009

    • Author(s)
      J.O'Rourke
    • Organizer
      Discrete Differential Geometry
    • Place of Presentation
      Oberwolfach (Germany)
    • Year and Date
      2009-01-16
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] リーマン多様体の最小跡と関連する諸問題2008

    • Author(s)
      伊藤 仁一
    • Organizer
      鹿児島大学数学談話会
    • Place of Presentation
      鹿児島大学理学部
    • Year and Date
      2008-12-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] リーマン多様体の最小跡と関連する諸問題2008

    • Author(s)
      伊藤 仁一
    • Organizer
      菅原邦雄先生・兼田英二先生の還暦記念研究会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-12-06
    • Related Report
      2008 Annual Research Report
  • [Presentation] 直観幾何学のいくつかのトピックス--数学教育専修における研究として--2008

    • Author(s)
      伊藤 仁一
    • Organizer
      数理研共同研究「数学教師に必要な数学能力形成に関する研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-12-03
    • Related Report
      2008 Annual Research Report
  • [Presentation] Thread construction of quadric (hyper) surfaces2008

    • Author(s)
      伊藤仁一
    • Organizer
      日本数学会秋季総合分科会幾何学分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-25
    • Related Report
      2010 Final Research Report
  • [Presentation] 楕円体のカットローカスと共役跡2008

    • Author(s)
      清原一吉
    • Organizer
      日本数学会秋季総合分科会応用数学分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-25
    • Related Report
      2010 Final Research Report 2008 Annual Research Report
  • [Presentation] Thread construction of quadric (hyper) surfaces2008

    • Author(s)
      伊藤 仁一
    • Organizer
      日本数学会秋季総合分科会応用数学分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] 二重多面体から得られる3時限空間充填立体2008

    • Author(s)
      奈良 知恵
    • Organizer
      日本数学会秋季総合分科会応用数学分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Annual Research Report
  • [Presentation] Thread construction of quadric (hyper) surfaces2008

    • Author(s)
      伊藤仁一
    • Organizer
      Discrete & Convex Geometry Workshop
    • Place of Presentation
      Renyi Inst.of Math.Budapest(Hungary)
    • Year and Date
      2008-07-05
    • Related Report
      2010 Final Research Report
  • [Presentation] Thread construction of quadric (hyper)surfaces2008

    • Author(s)
      J. Itoh
    • Organizer
      Discrete & Convex Geometry Workshop
    • Place of Presentation
      Renyi Inst. of Math. Budapest (Hungary)
    • Year and Date
      2008-07-05
    • Related Report
      2008 Annual Research Report
  • [Presentation] Space-filling polyhedra with reflectiveness2008

    • Author(s)
      C. Nara
    • Organizer
      Discrete & Convex Geometry Workshop
    • Place of Presentation
      Renyi Inst. of Math. Budapest (Hungary)
    • Year and Date
      2008-07-05
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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