Periodic Geodesics and Geometry of Compact Lorentzian Manifolds with a Killing Vector Field

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dc.creatorFlores, Jose Luis
dc.creatorJavaloyes, Miguel Angel
dc.creatorPiccione, Paolo
dc.date2008-12-05
dc.date2009-02-25
dc.date.accessioned2026-07-07T12:46:05Z
dc.date.available2026-07-07T12:46:05Z
dc.descriptionWe 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 a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold $M$ admits a Lorentzian metric with a never vanishing Killing vector field which is timelike somewhere if and only if $M$ admits a smooth circle action without fixed points.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/0812.1163
dc.identifierhttp://arxiv.org/abs/0812.1163
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221265
dc.subjectDifferential Geometry
dc.subject53C22, 53C50, 53C12
dc.titlePeriodic Geodesics and Geometry of Compact Lorentzian Manifolds with a Killing Vector Field
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