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Proceedings of the American Mathematical Society

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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 | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

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  • [2] C. Conley, Invariant sets which carry a one form, J. Differential Equations 8 (1970), 587-594. MR 43 #5122. MR 0279400 (43:5122)
  • [3] F. Brock Fuller, The existence of periodic points, Ann. of Math. (2) 57 (1953), 229-230. MR 14, 669. MR 0052764 (14:669f)
  • [4] D. Tischler, On fibering certain foliated manifolds over $ {S^1}$, Topology 9 (1970), 153-154. MR 41 #1069. MR 0256413 (41:1069)

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Additional Information

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

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