| 书目名称 | Vector Fields on Manifolds | | 编辑 | Michael F. Atiyah | | 视频video | | | 丛书名称 | Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen | | 图书封面 |  | | 描述 | This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extens ions of Hopf‘s theorem to the case r > 1. Arecent article by E. Thomas [10] gives a good survey of work in this general area. Our approach to these problems is based on the index theory of elliptic differential operators and is therefore rather different from the standard topological approach. Briefly speaking, what we do is to observe that certain invariants of a manifold (Euler characteristic, signature, etc. ) are indices of elliptic operators (see [5]) and the existence of a certain number of vector fields implies certain symmetry conditions for these operators and hence corresponding results for their indices. In this way we obtain certain necessary conditions for the existence of vector fields and, more generally , for the existence of fields of tangent planes. For example, one of our results is the follow | | 出版日期 | Book 1970 | | 关键词 | Area; DEX; Euler characteristic; Invariant; Signatur; Vector field; boundary element method; character; diff | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-322-98503-3 | | isbn_softcover | 978-3-322-97941-4 | | isbn_ebook | 978-3-322-98503-3 | | copyright | Springer Fachmedien Wiesbaden 1970 |
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发表于 2025-3-21 16:32:42
