Vector Fields on Manifolds

Part of the Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen book series (AFLNW, volume 200)


This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of existence 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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Topology of Elliptic Operators

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Copyright information

© Springer Fachmedien Wiesbaden 1970

Authors and Affiliations

  1. 1.Oxford UniversityUK

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