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Differential geometric research of regular surfaces in a wider sense

Research Project

Project/Area Number 17K05227
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionTokyo Denki University

Principal Investigator

KOKUBU Masatoshi  東京電機大学, 工学部, 教授 (50287439)

Project Period (FY) 2017-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords曲面 / 広義正則曲面 / 特異点 / 微分幾何 / 平均曲率 / 正則性 / 幾何学
Outline of Final Research Achievements

In the academic year 2017--2019, five co-authored papers were published and one pre-print is published on the web (arXiv for math). They give a generalization distinguished from the known theory of surfaces.
The contents of the papers are researches on surfaces with singularities and mixed-type surface of spacelike-type and timelike-type. These surfaces belong to the class of `regular surfaces in a wider sense' of our theme. We studied them paying attention to mean curvature which is a differential geometric invariant.

Academic Significance and Societal Importance of the Research Achievements

本研究の意義は,これまで研究されてこなかった対象に焦点を当て,いくつかの命題を示すことにより,微分幾何的曲面論における新たな側面を与えたことと言えよう.
新たな概念として「広義の正則曲面」を提唱し,広義の正則曲面およびその曲面から生じる幾何構造を研究すること,およびそれらの普遍的な理論の構築を最終目標として始められたものである.最終目標に近づくことができたことで,微分幾何的曲面論における新たな研究分野を与えることができた.

Report

(4 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (7 results)

All 2020 2018 2017

All Journal Article (5 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 5 results,  Open Access: 5 results,  Acknowledgement Compliant: 1 results) Presentation (2 results) (of which Int'l Joint Research: 1 results,  Invited: 2 results)

  • [Journal Article] Analytic extension of exceptional constant mean curvature one catenoids in de Sitter 3-space2020

    • Author(s)
      Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara and Kotaro Yamada
    • Journal Title

      Mathematical Journal of Okayama University

      Volume: 62

    • NAID

      120006778830

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Addendum: Singularities of flat fronts in hyperbolic space2018

    • Author(s)
      Kokubu Masatoshi、Rossman Wayne、Saji Kentaro、Umehara Masaaki、Yamada Kotaro
    • Journal Title

      Pacific Journal of Mathematics

      Volume: 294 Issue: 2 Pages: 505-509

    • DOI

      10.2140/pjm.2018.294.505

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Quadrics and Scherk towers2017

    • Author(s)
      Fujimori S.、Hertrich-Jeromin U.、Kokubu M.、Umehara M.、Yamada K.
    • Journal Title

      Monatshefte f?r Mathematik

      Volume: - Issue: 2 Pages: 249-279

    • DOI

      10.1007/s00605-017-1075-5

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Mixed type surfaces with bounded mean curvature in 3-dimensional space-times2017

    • Author(s)
      A. Honda, M. Koiso, M. Kokubu, M. Umehara and Kotaro Yamada
    • Journal Title

      Diff. Geom. and its Appl.

      Volume: 52 Pages: 64-77

    • DOI

      10.1016/j.difgeo.2017.03.009

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Analytic extension of Jorge-Meeks type maximal surfaces in Lorentz-Minkowski 3-space2017

    • Author(s)
      Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara and Kotaro Yamada
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 54 Pages: 249-272

    • NAID

      120006312701

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] R^3, R^3_1 の曲面に関する Kenmotsu 型公式の統一化と応用2018

    • Author(s)
      國分 雅敏
    • Organizer
      部分多様体論・湯沢2018
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Kenmotsu-type formulas -- Unification and Application2017

    • Author(s)
      Masatoshi Kokubu
    • Organizer
      International Workshop on Differential Geometric Aspects of Integrable Systems
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited

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Published: 2017-04-28   Modified: 2021-02-19  

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