Periodic Geodesics and Geometry of Compact Stationary Lorentzian Manifolds
نویسنده
چکیده
We prove the existence of at least two timelike non self-intersecting periodic geodesics in compact stationary Lorentzian manifolds and we discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a stationary Lorentzian metric if and only if M admits a smooth circle action without fixed points.
منابع مشابه
Periodic Geodesics and Geometry of Compact Lorentzian Manifolds with a Killing Vector Field
We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is never vanishing, then there are at least two distinct periodic geodesics; as ...
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