Sufficient conditions for periodicity of a Killing vector field
HTML articles powered by AMS MathViewer
- by Walter C. Lynge PDF
- Proc. Amer. Math. Soc. 38 (1973), 614-616 Request permission
Abstract:
Let $X$ be a complete Killing vector field on an $n$-dimensional connected Riemannian manifold. Our main purpose is to show that if $X$ has as few as $n$ closed orbits which are located properly with respect to each other, then $X$ must have periodic flow. Together with a known result, this implies that periodicity of the flow characterizes those complete vector fields having all orbits closed which can be Killing with respect to some Riemannian metric on a connected manifold $M$. We give a generalization of this characterization which applies to arbitrary complete vector fields on $M$.References
- Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 614-616
- MSC: Primary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-1973-0317230-3
- MathSciNet review: 0317230