An affine immersion from a manifold with certain structures on itstangent bundle and its application
| Project/Area Number |
23740060
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
KUROSU Sanae 東京理科大学, 理学部, 理学部 (70457844)
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| Project Period (FY) |
2011 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| 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)
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| 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 |
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| 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.
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Report
(3 results)
Research Products
(4 results)
