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A study on a generating function of a complex Lagrangian submanifold and its applications

Research Project

Project/Area Number 22540103
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

EJIRI Norio  名城大学, 理工学部, 教授 (80145656)

Co-Investigator(Renkei-kenkyūsha) OZAWA Tetuya  名城大学, 理工学部, 教授 (20169288)
HASHIMOTO Hideya  名城大学, 理工学部, 教授 (60218419)
Project Period (FY) 2010-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2014: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2013: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2012: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords複素ラグランジュ錐の生成関数 / 平坦トーラスの極小曲面 / 極小曲面の変形空間 / ヤコビ作用素 / index and nullity / null submanifold / horizontal submanifold / ruled submanifold / 複素ラグランジュ錐 / 生成関数 / 3重周期的極小曲面 / モース指数 / 種数3の超楕円面 / 種数4の超楕円面 / 2重周期的極小曲面 / 極小曲面 / 平坦トーラス / Jacobi operator / Schwarz' P 曲面 / Gyroid / Schwarz' P 曲面 / Schwarz'P曲面 / P曲面 / CMC安定
Outline of Final Research Achievements

We study a generating function of complex Lagrangian submanifold and get the relation with other submanifolds. In particular, by the relation between a generating function of a complex Lagrangian cone and a special pseudo kaehler structure, we obtain an algorithm to compute the index and the nullity of a compact, orientable, minimal surface in a torus by the periods of Abelian differentials of the first kind and the second kind. Concretely, we can seek the index and the nullity of Schwarz' P family, D family and H family.

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

    (11 results)

All 2014 2013 2012 2011

All Journal Article (3 results) (of which Peer Reviewed: 3 results) Presentation (8 results) (of which Invited: 3 results)

  • [Journal Article] Ruled complex Lagrangian submanifolds of dimension two in {\bf C}^42013

    • Author(s)
      Norio Ejiri
    • Journal Title

      Prospects of Differential Geometry and its Related Fields

      Volume: 2 Pages: 213-225

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a moduli theory of minimal surfaces2013

    • Author(s)
      Norio Ejiri and Toshihiri Shoda
    • Journal Title

      Prospects of Differential Geometry and its Related Fields

      Volume: 2 Pages: 155-172

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A remark on complex Lagrangian cones in H^n2011

    • Author(s)
      N.Ejiri, K.Tsukada
    • Journal Title

      Recent Progress in Differential Geometry and its related fields

      Pages: 151-157

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] 3重周期的極小曲面の退化極限2014

    • Author(s)
      江尻典雄、藤森祥一(講演者)、庄田敏宏
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Annual Research Report
  • [Presentation] On limits of triply periodic minimal surfaces of genus 32014

    • Author(s)
      江尻典雄
    • Organizer
      研究集会「四元数複素微分幾何学とその周辺/Quaternionic complex differential geometry and related topics」
    • Place of Presentation
      お茶の水女子大学
    • Year and Date
      2014-09-04
    • Related Report
      2014 Annual Research Report
  • [Presentation] The deformation space of a compact orientable minimal surface in a torus2014

    • Author(s)
      Norio Ejiri
    • Organizer
      The second Japanese-Spanish Workshop on Differential Geometry
    • Place of Presentation
      Tokyo Institute of Technology
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Ruled complex Lagrangian submanifolds of dimension two in {\bf C}^42013

    • Author(s)
      Norio Ejiri
    • Organizer
      International Workshop on Special Geometry and Minimal Submanifolds
    • Place of Presentation
      Tohoku University
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Minimal surfaces of genus 3 in T^32012

    • Author(s)
      江尻典雄
    • Organizer
      名城大学幾何学研究集会「極小曲面と幾何構造」
    • Place of Presentation
      名城大学
    • Year and Date
      2012-03-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] H^n内の複素ラグランジュ部分多様体について2012

    • Author(s)
      江尻典雄
    • Organizer
      RIMS研究集会 部分多様体と四元数構造
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] トーラス内の極小曲面の変形空間上のspecial pseudo Kaehler structureとその応用2011

    • Author(s)
      江尻典雄
    • Organizer
      京都大学数理解析研究所「部分多様体の微分幾何学的研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-06-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] Special pseudo Kaehler metrics, signature, index on a deformation space of minimal surfaces in tori2011

    • Author(s)
      Norio Ejiri
    • Organizer
      国際研究集会 Differential Geometry and Tanaka Theory~Differential System and hypersurface Theory~
    • Place of Presentation
      京都大学数理解析研究所(京都)
    • Year and Date
      2011-01-24
    • Related Report
      2010 Annual Research Report

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

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