• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

The geometry of geodesics and its application to the discrete mathematics

Research Project

Project/Area Number 22540072
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

INNAMI Nobuhiro  新潟大学, 自然科学系, 教授 (20160145)

Project Period (FY) 2010-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords測地線 / 曲面 / ボロノイ図 / カットローカス / シュタイナー比 / 平面凸ビリヤード問題 / トポノゴフの比較定理 / 球面定理 / リーマン幾何学 / 曲面上の幾何学 / 最小点軌跡 / サブ混合性 / 曲面のボロノイ図 / サブエルゴード性 / 距離関数の差 / 最短ネットワーク / 測地流 / エルゴード性 / 円のリヤード / 最小シュタイナー木 / 測地線の幾何学 / トポノゴフの定理 / コンジュゲートローカス / 極
Outline of Final Research Achievements

In an intrinsic metric space, a locally minimizing curve is called a geodesic. We say that a metric space is a geodesic space if any two points can be joined by a minimizing geodesic. H. Busemann put forward the geometry of geodesics in 1955 to study some properties of geodesics, the topological and metric structure of spaces. Using his methods, we produced results on the studies of sets of poles in a Riemannian manifold, the geodesic flows on surfaces and the plane convex billiard ball problems, the Steiner ratio problem for surfaces, a generalization of Toponogov's comparison theorem and some sphere theorems, the relation of a Voronoi diagram and the cut locus. We have a prospect to develop the geometry of geodesics in a non-symmetric intrinsic distance space.

Report

(6 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (22 results)

All 2015 2014 2013 2012 2011 2010 Other

All Journal Article (13 results) (of which Peer Reviewed: 13 results,  Acknowledgement Compliant: 3 results) Presentation (9 results) (of which Invited: 1 results)

  • [Journal Article] Angular distribution of diameters for spheres and rays for planes2015

    • Author(s)
      Nobuhiro Innami and Yuya Uneme
    • Journal Title

      Pacific J. Math.

      Volume: 印刷中

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The cut locus and Voronoi diagram of a finite set of points in a surface (2015) (22 pages)2015

    • Author(s)
      N. Innami, K. Shiohama and Y. Uneme
    • Journal Title

      manuscripta math.

      Volume: 印刷中 Issue: 1-2 Pages: 243-264

    • DOI

      10.1007/s00229-015-0733-y

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The front of increasing concentric balls and cut locus in a surface2014

    • Author(s)
      N. Innami, K Shiohama and Y. Uneme
    • Journal Title

      Diff. Geom. Appl.

      Volume: 34 Pages: 80-86

    • DOI

      10.1016/j.difgeo.2014.04.001

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Differentiability of invariant circles for strongly integrable convex billiards2013

    • Author(s)
      Nobuhiro Innami
    • Journal Title

      Nihonkai Math. J.

      Volume: 24 Pages: 1-17

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Complete real hypersurfaces and special K-line bundles in K-hyperbolic spaces2013

    • Author(s)
      Nobuhiro Innami, You Itokawa, Katsuhiro Shiohama
    • Journal Title

      International J. Math.

      Volume: 24

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Alexandrov-Toponogov comparison theorem for radial curvature2013

    • Author(s)
      Nobuhiro Innami, Katsuhiro Shiohama, Yuya Uneme
    • Journal Title

      Nihonkai Math. J.

      Volume: 24 Pages: 57-91

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A sphere theorem for radial curvature2013

    • Author(s)
      Nobuhiro Innami, Katsuhiro Shiohama, Yuya Uneme
    • Journal Title

      Nihonkai Math. J.

      Volume: 24 Pages: 93-102

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A comparison theorem for Steiner minimum trees in surfaces with curvature bounded below2013

    • Author(s)
      Shintaro Naya
    • Journal Title

      Tohoku Math. J.

      Volume: 65 Pages: 131-157

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The cut loci, conjugate loci and poles in a complete Riemannian manifold2012

    • Author(s)
      Nobuhiro Innami
    • Journal Title

      Geom. Funct. Anal.

      Volume: 22 Pages: 1400-1406

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rays and souls in von Mangoldt planes2012

    • Author(s)
      Igor Belegradek
    • Journal Title

      Pacific J. Math.

      Volume: 259 Pages: 279-306

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The asymptotic behavior of geodesic circles in a 2-torus of revolution and a sub-ergodic property2012

    • Author(s)
      Nobuhiro Innami
    • Journal Title

      Nihonkai Math. J.

      Volume: 23 Pages: 43-55

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Metric spheres in the projective spaces with constant holomor phic sectional curvature2011

    • Author(s)
      Innami, Nobuhiro
    • Journal Title

      Tsukuba J.Math

      Volume: 35 Pages: 79-90

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Steiner ratio conjecture of Gilbert-Pollak may still be open2010

    • Author(s)
      Nobuhiro Innami
    • Journal Title

      Algorithmica

      Volume: 57 Pages: 869-872

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] フィンスラー計量を持つ回転トーラス上の測地線2015

    • Author(s)
      印南信宏
    • Organizer
      日本数学会年会
    • Place of Presentation
      明治大学(東京都・千代田区神田駿河台)
    • Year and Date
      2015-03-24
    • Related Report
      2014 Annual Research Report
  • [Presentation] 曲面上のボロノイ図とカットローカス2015

    • Author(s)
      印南信宏
    • Organizer
      研究集会「直観幾何学」
    • Place of Presentation
      熊本大学(熊本県・熊本市中央区黒髪)
    • Year and Date
      2015-03-10
    • Related Report
      2014 Annual Research Report
  • [Presentation] 曲面上の測地円とカットローカス2015

    • Author(s)
      印南信宏
    • Organizer
      研究会「測地線及び関連する諸問題
    • Place of Presentation
      熊本大学(熊本県・熊本市中央区黒髪)
    • Year and Date
      2015-01-10
    • Related Report
      2014 Annual Research Report
  • [Presentation] Three distances induced from a Finsler metric and their geodesics in a 2-torus2014

    • Author(s)
      Nobuhiro Innami
    • Organizer
      The 49th Symposium on Finsler Geometry
    • Place of Presentation
      長崎産業会館(長崎県・長崎市大黒町)
    • Year and Date
      2014-12-05
    • Related Report
      2014 Annual Research Report
  • [Presentation] フィンスラー計量から導入される3つの距離とその測地線2014

    • Author(s)
      印南信宏
    • Organizer
      福岡大学微分幾何研究会
    • Place of Presentation
      福岡大学セミナーハウス(福岡県・福岡市中央区六本松)
    • Year and Date
      2014-11-01
    • Related Report
      2014 Annual Research Report
  • [Presentation] 多角形に関するシュタイナー比の比較定理2013

    • Author(s)
      印南信宏
    • Organizer
      研究会「直観幾何学」
    • Place of Presentation
      熊本大学教育学部
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 平面凸ビリヤードの不変円の微分可能性について2011

    • Author(s)
      印南信宏
    • Organizer
      研究集会「部分多様体幾何とリー群作用2011」
    • Place of Presentation
      東京理科大学森戸記念館
    • Year and Date
      2011-09-03
    • Related Report
      2011 Annual Research Report
  • [Presentation] ラジアル曲率によるトポノゴフの比較定理2011

    • Author(s)
      印南信宏
    • Organizer
      研究集会「リーマン幾何と幾何解析」
    • Place of Presentation
      筑波大学
    • Year and Date
      2011-02-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] 回転面を参照した球面定理

    • Author(s)
      印南信宏
    • Organizer
      研究集会「測地線及び関連する諸問題」
    • Place of Presentation
      熊本大学教育学部
    • Related Report
      2013 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi