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2012 Fiscal Year Final Research Report

Almost Hermitian geometry and the related topics

Research Project

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Project/Area Number 22540071
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

SEKIGAWA Kouei  新潟大学, 自然科学系, フェロー (60018661)

Co-Investigator(Kenkyū-buntansha) OGURO Takashi  東京電機大学, 理工学部, 講師 (40297578)
YAMADA Akira  長岡工業高等専門学校, 一般教育科, 准教授 (60311007)
Project Period (FY) 2010 – 2012
Keywords概エルミート多様体 / ゴールドバーグの予想 / チャーン・ヴェイユ理論 / ガウス・ボンネ・チャーンの定理 / アインシュタイン・ヒルベルト汎関数 / 単位接球面束 / 普遍曲率恒等式 / ボッホナー曲率テンンソル
Research Abstract

An almost complex manifold quipped with a compatible Riemannian metric is called an almost Hermitian manifold. In our research project, we obtained several interesting results on the topics concerning the integrability of almost Hemitian manifolds and also on various variational problems for the Koda functional which is regarded as an extension of the Einstein-Hilbert functional to almost Hermitian setting. Further,we obtained some results on the unit tangent sphere bundles such that the characteristic vector fields are harmonic vector fields. We also discussed some problems arised in the course of our research activity and could obtain unexpected results.

  • Research Products

    (19 results)

All 2013 2012 2011 2010

All Journal Article (14 results) (of which Peer Reviewed: 14 results) Presentation (5 results)

  • [Journal Article] Transplanting geometrical structures2013

    • Author(s)
      Y.Euh,P.Gilkey,J.H.Park,K.Sekigawa
    • Journal Title

      Diff.Geom.Appl

      Volume: 31 Pages: 374-387

    • DOI

      DOI:10.1016/j.diffeo.2013.03.006

    • Peer Reviewed
  • [Journal Article] Some critical almost Hermitian structures2013

    • Author(s)
      J.C.Lee,J.H.Park,K.Sekigawa
    • Journal Title

      Results. Math

      Volume: 63 Pages: 31-45

    • DOI

      DOI:10.1007/S00025-011-0143-8

    • Peer Reviewed
  • [Journal Article] A curvature identity on a 4-dimensionalRiemannian manifold2013

    • Author(s)
      Y.Euh, J.H.Park, K.Sekigawa
    • Journal Title

      Results. Math

      Volume: 63 Pages: 107-114

    • DOI

      DOI:10.1007/S00025-011-0164-3

    • Peer Reviewed
  • [Journal Article] Orthogonal almost complex structures onThe Riemannian products ofeven-dimensional round spheres2013

    • Author(s)
      Y.Euh, K.Sekigawa
    • Journal Title

      J.Korean Math.Soc

      Volume: 50 Pages: 231-240

    • DOI

      DOI:10.4134/JKMS.2013.50.2.231

    • Peer Reviewed
  • [Journal Article] Universal curvature identities2012

    • Author(s)
      P.Gilkey, J.H.Park, K.Sekigawa
    • Journal Title

      J.Geom. Phys

      Volume: 62 Pages: 814-825

    • DOI

      DOI:10.1016/j.geomphys.2012.01.002

    • Peer Reviewed
  • [Journal Article] Hermitian structures on the product of Sasakian manifolds2012

    • Author(s)
      J.C.Lee, J.H.Park, K.Sekigawa
    • Journal Title

      Geometriae Dedicata

      Volume: 161 Pages: 399-408

    • DOI

      DOI:10.1007/s10711-012-9711-7

    • Peer Reviewed
  • [Journal Article] Notes on some classes of 3-dimensional Contact metricmanifolds2012

    • Author(s)
      J.E.Jin, J.H.Park, K.Sekigawa
    • Journal Title

      Balkan J. Geom. Appl

      Volume: 17 Pages: 54-65

    • Peer Reviewed
  • [Journal Article] Universal curvature identities2011

    • Author(s)
      P.Kilkey, J.H.Park, K.Sekigawa
    • Journal Title

      Diff. Geom. Appl

      Volume: 29 Pages: 770-778

    • DOI

      DOI:10.1016/j.difgeo.2011.08.005

    • Peer Reviewed
  • [Journal Article] Critical metrics for quadratic functionals In the curvature on 4-dimensional Manifolds2011

    • Author(s)
      Y.Euh, J.H.Park, K.Sekigawa
    • Journal Title

      Diff. Geom. Appl

      Volume: 29 Pages: 642-646

    • DOI

      DOI:10.1016/j.difgeo.2011.07.001

    • Peer Reviewed
  • [Journal Article] H-contact unit tangent sphere bundles of four-dimensional Riemannian manifolds2011

    • Author(s)
      S.H.Chun, J.H.Park, K.Sekigawa
    • Journal Title

      J. Aust. Math. Soc

      Volume: 91 Pages: 243-256

    • DOI

      DOI:10.1017/S1446788711001388

    • Peer Reviewed
  • [Journal Article] Almost Hermitian surfaces With vanishing Tricerri-Vanhecke Bochner curvature tensor2011

    • Author(s)
      Y.Euh,J.C.Lee,J.H.Park,K.Sekigawa, A.Yamada
    • Journal Title

      Colloq.Math

      Volume: 122 Pages: 33-53

    • DOI

      DOI:10.4064/cm122-1-4

    • Peer Reviewed
  • [Journal Article] Nootes on strictly nearly Kaehler Einstein manifolds2011

    • Author(s)
      Y.Euh, K.Sekigawa
    • Journal Title

      Compt. Rend. de Acad. Sci

      Volume: 64 Pages: 791-798

    • Peer Reviewed
  • [Journal Article] H-contact unit tangent sphere bundles of Einstein manifolds2011

    • Author(s)
      S.H.Chun, J.H.Park, K.Sekigawa
    • Journal Title

      Q. J. Math

      Volume: 62 Pages: 59-69

    • DOI

      DOI:10.1093/qmath/hap025

    • Peer Reviewed
  • [Journal Article] Notes on critical almost Hermitian Structures2010

    • Author(s)
      J.C.Lee, J.H.Park, K.Sekigawa
    • Journal Title

      Bull. Korean Math. Soc

      Volume: 47 Pages: 167-178

    • DOI

      DOI:10.4134/BKMS,2010.47.1.167

    • Peer Reviewed
  • [Presentation] 4次元リーマン多様体の普遍曲率恒等式2012

    • Author(s)
      関川浩永
    • Organizer
      第6回数物研究会
    • Place of Presentation
      富山県民会館
    • Year and Date
      2012-09-13
  • [Presentation] A curvature identity ona 4-dimensional Riemannianmanifold and its applications2010

    • Author(s)
      関川浩永
    • Organizer
      Conference in Geometryand Global Analysis
    • Place of Presentation
      サンティアゴ・デ・コンポステラ(スペイン)
    • Year and Date
      2010-12-13
  • [Presentation] 臨界概エルミート構造について2010

    • Author(s)
      関川浩永
    • Organizer
      放送大学秋田学習センター
    • Year and Date
      2010-11-18
  • [Presentation] Some critical almost Hermitian structures and examples2010

    • Author(s)
      関川浩永
    • Organizer
      Intrnational workshop on complex structures,integrability and vector fields
    • Place of Presentation
      ソフィア(ブルガリア)
    • Year and Date
      2010-09-15
  • [Presentation] A curvature identity on a 4-dimensional Riemannian manifold2010

    • Author(s)
      関川浩永
    • Organizer
      International Workshop on Differential Geometry
    • Place of Presentation
      成均館大学校(韓国)
    • Year and Date
      2010-06-25

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Published: 2014-08-29  

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