Sufficient conditions for periodicity of a Killing vector field
Abstract: Let be a complete Killing vector field on an -dimensional connected Riemannian manifold. Our main purpose is to show that if has as few as closed orbits which are located properly with respect to each other, then 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 . We give a generalization of this characterization which applies to arbitrary complete vector fields on .
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Keywords: Killing vector field, isometry, flow, Lie algebra, Riemannian metric, Riemannian manifold, closed orbit, minimizing geodesic
Article copyright: © Copyright 1973 American Mathematical Society