Parallel vector fields and periodic orbits
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- Proc. Amer. Math. Soc. 44 (1974), 167-168 Request permission
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
- Richard C. Churchill, Invariant sets which carry cohomology, J. Differential Equations 13 (1973), 523โ550. MR 331433, DOI 10.1016/0022-0396(73)90010-7
- C. Conley, invariant sets which carry a one-form, J. Differential Equations 8 (1970), 587โ594. MR 279400, DOI 10.1016/0022-0396(70)90032-X
- F. B. Fuller, The existence of periodic points, Ann. of Math. (2) 57 (1953), 229โ230. MR 52764, DOI 10.2307/1969856
- D. Tischler, On fibering certain foliated manifolds over $S^{1}$, Topology 9 (1970), 153โ154. MR 256413, DOI 10.1016/0040-9383(70)90037-6
Additional Information
- © Copyright 1974 American Mathematical Society
- 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