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Titlebook: Vector Fields on Manifolds; Michael F. Atiyah Book 1970 Springer Fachmedien Wiesbaden 1970 Area.DEX.Euler characteristic.Invariant.Signatu

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發(fā)表于 2025-3-21 16:32:42 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Vector Fields on Manifolds
編輯Michael F. Atiyah
視頻videohttp://file.papertrans.cn/981/980835/980835.mp4
叢書名稱Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen
圖書封面Titlebook: Vector Fields on Manifolds;  Michael F. Atiyah Book 1970 Springer Fachmedien Wiesbaden 1970 Area.DEX.Euler characteristic.Invariant.Signatu
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
關(guān)鍵詞Area; DEX; Euler characteristic; Invariant; Signatur; Vector field; boundary element method; character; diff
版次1
doihttps://doi.org/10.1007/978-3-322-98503-3
isbn_softcover978-3-322-97941-4
isbn_ebook978-3-322-98503-3
copyrightSpringer Fachmedien Wiesbaden 1970
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eformen bereit: Flüssige Brennstoffe, Gas und Elektrizit?t. Wie aus Abbildung 11.) zu ersehen ist, kommen für einen wesentlichen Leuchtgaskonsum nur die St?dte München, Nürnberg und Augsburg in Frage. Die Wertung der Gaswerke als W?rmeenergiequelle geschah bereits in anderem Zusammenhang. Die bisher
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地板
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Book 1970 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
6#
發(fā)表于 2025-3-22 12:55:04 | 只看該作者
ds 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 follow978-3-322-97941-4978-3-322-98503-3
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https://doi.org/10.1007/978-3-322-98503-3Area; DEX; Euler characteristic; Invariant; Signatur; Vector field; boundary element method; character; diff
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978-3-322-97941-4Springer Fachmedien Wiesbaden 1970
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Vector Fields on Manifolds,e 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 extensions of Hopfs theorem to the case r > 1. A recent article by E. Thomas [10] gives a good survey of work in this general area.
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