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Global Analysis of Manifolds and Conformal Structures

流形和共形结构的全局分析

基本信息

批准号：
08304005
负责人：
ITOH Mitsuhiro
金额：
$ 9.41万
依托单位：
UNIVERSITY OF TSUKUBA
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1997
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08304005/
关键词：
MANIFOLD CONFORMAL STRUCTURE DIFFERENTIAL GEOMETRY 自己双対計量接触構造 Einstein-Weyl多様体

项目摘要

The purposes of this research project was to accomplish synthetic investigation for geometry of manifolds, mainly for conformal structures and to obtain progressive reserach results.By considering the last year's research progress situation we held in August, 1997 the geometry symposium, greatly organized, on a nationwide scale (participants 251, survey lectures 3, ordinary talks 53). In this symposium we could get exchanging of informations among researchers and intension and broadening of researches related to the purposes. As its consequences, for the research of global analysis on conformal structures M.Itoh, myself, the chief researcher, together with coresearchers, K.Akutagawa, S.Nayatani, Y.Izeki, S.Kato were able to obtain plenty of researches on the whole conformal geometry covering self-dual 4-manifolds, conformally flat manifolds and Einstein-Weyl manifolds.In the other areas, that is, geometry of vector bundles, gauge fields great contributions were done by this project, especially in the field of self-dual bundles on quaternionic Kaehler manifolds. And also investigations done by this project took a progressive step in the direction of (almost) Kaehler structures. Furthermore, homogeneous manifolds, Rie-mannian geometry, symplectic geometry, geometry of curves and surfaces could get research progresses.

本研究课题的目的是完成流形几何的综合研究，主要是共形结构的综合研究，并取得进展性的研究成果，我们考虑到去年的研究进展情况，于1997年8月在全国范围内大规模地组织召开了几何专题讨论会（参加者251人，综述讲座3次，一般讨论53次）。通过这次研讨会，我们可以了解到研究者之间的信息交流以及与目的相关的研究的内涵和广度。其结果是，对于共形结构的全局分析研究，我本人、首席研究员伊藤先生以及共同研究员K.Akutagawa、S.Nayatani、Y.Izeki、S.Kato能够对整个共形几何进行大量研究，涵盖自对偶4-流形、共形平坦流形和Einstein-Weyl流形。在其他领域，即向量丛几何，该项目在规范场的研究中做出了巨大的贡献，特别是在四元数Kaehler流形上的自对偶丛领域。该项目所做的调查也朝着（几乎）Kaehler结构的方向迈出了一步。在齐次流形、黎曼几何、辛几何、曲线曲面几何等方面也取得了研究进展。