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Affine immersions in various fields

Research Project

Project/Area Number 26400058
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionHokkaido University

Principal Investigator

FURUHATA Hitoshi  北海道大学, 理学研究院, 准教授 (80282036)

Co-Investigator(Renkei-kenkyūsha) FUJIOKA Atsushi  関西大学, システム理工学部, 教授 (30293335)
Research Collaborator HASEGAWA Izumi  
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords射影はめ込み / 中心アファインはめ込み / 統計多様体 / 正則統計多様体 / CR部分多様体 / 佐々木統計多様体 / 剱持統計多様体 / 中心アファイン曲面 / 線織面 / 中心写像 / 概接触計量多様体 / 剱持多様体 / 捩じれ積 / 佐々木多様体 / 部分多様体 / アファインはめ込み / 射影曲面 / 断面曲率 / CR部分多様体
Outline of Final Research Achievements

We showed that a nondegenerate surface in the projective 3-space is locally constructed from a centroaffine minimal surface in the 4-dimensional vector space. The condition for such a surface to be projectively applicable to an affine sphere was obtained. We determined a nondegenerate centroaffine ruled surface such that the image of its center map lies on a plane containing the origin.
We defined the sectional curvature for a statistical structure, and found several properties of CR statistical submanifolds in a holomorphic statistical manifold of constant holomorphic sectional curvature, which are similar to well-known results for CR submanifolds in a Kaehler space form. We introduced notions of Sasakian statistical structure and Kenmotsu statistical structure, and gave their interesting examples.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report

Research Products

(20 results)

All 2018 2017 2016 2015 2014 Other

All Int'l Joint Research Journal Article Presentation Remarks

  • [Int'l Joint Research] Jamia Millia Islamia University(India)

    • Related Report
      2016 Research-status Report
  • [Journal Article] The center map of a centroaffine ruled surface2018

    • Author(s)
      Fujioka A. and Furuhata H.
    • Journal Title

      An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.)

      Volume: 印刷中

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Kenmotsu statistical manifolds and warped product2017

    • Author(s)
      Furuhata H., Hasegawa I., Okuyama Y. and Sato K.
    • Journal Title

      J. Geom.

      Volume: 108 Pages: 1175-1191

    • DOI

      10.1007/s00022-017-0403-1

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sasakian Statistical Manifolds II2017

    • Author(s)
      Furuhata H.
    • Journal Title

      Lecture Notes in Comput. Sci.

      Volume: 10589 Pages: 179-185

    • DOI

      10.1007/978-3-319-68445-1_21

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sasakian statistical manifolds2017

    • Author(s)
      Furuhata H., Hasegawa I., Okuyama Y., Sato K. and Shahid, M.H.
    • Journal Title

      J. Geom. Phys.

      Volume: 117

    • DOI

      10.1016/j.geomphys.2017.03.010

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Projective surfaces and pre-normalized Blaschke immersions of codimension two2016

    • Author(s)
      Fujioka A. Furuhata H. and Sasaki T.
    • Journal Title

      Int. Electron. J. Geom.

      Volume: 9 Pages: 100-110

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Submanifold Theory in Holomorphic Statistical Manifolds2016

    • Author(s)
      Furuhata H. and Hasegawa I.
    • Journal Title

      Dragomir, S. et al. (eds.), Geometry of Cauchy-Riemann Submanifolds, Springer

      Volume: -

    • DOI

      10.1007/978-981-10-0916-7_7

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 佐々木構造をもつ統計多様体2017

    • Author(s)
      古畑仁
    • Organizer
      名城研究集会「多様体上の計量と幾何構造」
    • Place of Presentation
      名城大学(愛知県名古屋市)
    • Year and Date
      2017-03-01
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 剱持統計多様体2017

    • Author(s)
      古畑仁
    • Organizer
      関大微分幾何研究会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 中心写像から見た曲面の中心アファイン幾何学2017

    • Author(s)
      古畑仁
    • Organizer
      第64回幾何学シンポジウム
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Sasakian statistical manifolds II2017

    • Author(s)
      Furuhata H.
    • Organizer
      3rd conference on Geometric Science of Information
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Sasakian statistical manifolds and hypersurfaces2017

    • Author(s)
      Furuhata H.
    • Organizer
      PNU-HU Joint Symposium
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 正則統計多様体のCR部分多様体2015

    • Author(s)
      古畑仁
    • Organizer
      福岡大学微分幾何学研究集会
    • Place of Presentation
      福岡大学セミナーハウス(福岡県福岡市)
    • Year and Date
      2015-10-30
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Affine differential geometry and surfaces in the projective space2015

    • Author(s)
      Furuhata H.
    • Organizer
      Differential Geoemetry with Dajczer
    • Place of Presentation
      東京工業大学(東京都目黒区)
    • Year and Date
      2015-10-06
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 統計多様体の曲率2015

    • Author(s)
      古畑仁
    • Organizer
      ミニワークショップ 統計多様体の幾何学とその周辺 (7)
    • Place of Presentation
      北海道大学(北海道札幌市)
    • Year and Date
      2015-09-01
    • Related Report
      2015 Research-status Report
  • [Presentation] 正則統計多様体とその曲率2014

    • Author(s)
      古畑仁
    • Organizer
      RIMS共同研究「統計多様体の諸分野への応用」
    • Place of Presentation
      京都大学数理解析研究所(京都市)
    • Year and Date
      2014-11-19
    • Related Report
      2014 Research-status Report
    • Invited
  • [Remarks] ミニワークショップ「統計多様体の幾何学とその周辺」(9)

    • URL

      http://www.math.sci.hokudai.ac.jp/~furuhata/workshop/stat/17/

    • Related Report
      2017 Annual Research Report
  • [Remarks] ミニワークショップ 統計多様体の幾何学とその周辺 (8)

    • URL

      http://www.math.sci.hokudai.ac.jp/~furuhata/workshop/stat/16/

    • Related Report
      2016 Research-status Report
  • [Remarks] ミニワークショップ 統計多様体の幾何学とその周辺 (7)

    • URL

      http://www.math.sci.hokudai.ac.jp/~furuhata/workshop/stat/15/

    • Related Report
      2015 Research-status Report
  • [Remarks] ミニワークショップ 統計多様体の幾何学とその周辺 (6)

    • URL

      http://www.math.sci.hokudai.ac.jp/~furuhata/workshop/stat/14/

    • Related Report
      2014 Research-status Report

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Published: 2014-04-04   Modified: 2019-03-29  

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