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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Parallel vector fields and periodic orbits


Author: Sol Schwartzman
Journal: Proc. Amer. Math. Soc. 44 (1974), 167-168
MSC: Primary 58F20
DOI: https://doi.org/10.1090/S0002-9939-1974-0331434-6
MathSciNet review: 0331434
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Abstract: Let $ V$ be a parallel vector field on a compact Riemannian manifold without boundary. Suppose the Euler class over the reals of the normal bundle to $ V$ is different from zero. Then the flow defined by $ V$ has a periodic orbit.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0331434-6
Keywords: Periodic orbit, parallel vector field, Euler class, flow
Article copyright: © Copyright 1974 American Mathematical Society