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An affine immersion from a manifold with certain structures on itstangent bundle and its application

Research Project

Project/Area Number 23740060
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionTokyo University of Science

Principal Investigator

KUROSU Sanae  東京理科大学, 理学部, 理学部 (70457844)

Project Period (FY) 2011 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Keywords微分幾何 / 部分多様体論 / アファインはめ込み / 多重調和写像 / tt*構造 / (パラ)ケーラー多様体
Research Abstract

1. We characterize an affine immersion from a manifold with almost product structure or an almost complex structure to a real affine space whose affine fundamental form is Hermitian or anti-Hermitian with the structure. As an application, we study an isometric immersion of a para-Kaehler manifold or an almost product Riemannian manifold, which is a manifold with metric which is compatible with the structures. Especially, we classify a para-pluriharmonic isometric immersion from a complete para-Kaehler manifold of codimension one or two.
2. We find a new construction of a tt*-bundle structure associated with a harmonic map from a Riemann surface into a sphere, that is a collaboration work with Katsuhiro Moriya. This construction is related to the Clifford algebra.

Report

(3 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Research-status Report
  • Research Products

    (4 results)

All 2013 2012

All Journal Article (3 results) (of which Peer Reviewed: 3 results) Presentation (1 results)

  • [Journal Article] A characterization for a (2,0)-geodesic affine immersion2013

    • Author(s)
      Sanae Kurosu
    • Journal Title

      Results in Mathematics

      Volume: 63 Issue: 1-2 Pages: 115-128

    • DOI

      10.1007/s00025-011-0165-2

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A tt*-bundle associated with a harmonic map from a Riemann surface2012

    • Author(s)
      Katsuhiro Moriya ,Sanae Kurosu
    • Journal Title

      Differential Geometry and its Applications

      Volume: 30 Pages: 227-232

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Relative nullity distributions, an affine immersion from an almost product manifold and a para-pluriharmonic isometric immersion2012

    • Author(s)
      Sanae Kurosu
    • Journal Title

      Annals of Global Analysis and Geometry,

      Volume: 42 Issue: 3 Pages: 333-347

    • DOI

      10.1007/s10455-012-9315-3

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Presentation] 余次元2の多重調和アファインはめ込みの特徴付け2012

    • Author(s)
      黒須早苗
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2012 Annual Research Report 2012 Final Research Report

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Published: 2011-08-05   Modified: 2019-07-29  

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