2013 Fiscal Year Final Research Report
Geometry of vector bundles and submanifolds realized by harmonic maps
| Project/Area Number |
23540095
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Meiji University (2012-2013)
Kyushu University (2011) |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
TAKAHASHI Masaro 久留米工業高等専門学校, 一般科目理科系, 准教授 (70311107)
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| Project Period (FY) |
2011 – 2013
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| Keywords | ベクトル束 / 調和写像 / 正則写像 / ゲージ理論 / 部分多様体 / モジュライ空間 |
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| Research Abstract |
Though a generalization of Do Carmo-Wallach theory on moduli spaces of minimal immersions between spheres was achieved by me, I succeeded to refine it. To do so, I define a new equivalence relation of maps called gauge equivalence of maps. This gives a unified proof of results which were obtained in another ways. In addition, I described a moduli spaces of holomorphic isometric embeddings of complex projective lines into complex quadrics. Moreover, I defined a projectively flat immersions into complex Grassmannian and obtained some properties of projectively flat immersions.
On the other hand, I got principal curvatures of isoparametric hypersurfaces of compact symmetric spaces. Such hypersurfaces was defined by isoparametric functions induced from sections of vector bundles. Invariants of submanifolds are related to invariants of connections on vector bundles.
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