Artículos de revistas
Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field
Fecha
2011Registro en:
MATHEMATISCHE ZEITSCHRIFT, v.267, n.1/Fev, p.221-233, 2011
0025-5874
10.1007/s00209-009-0617-5
Autor
FLORES, Jose Luis
JAVALOYES, Miguel Angel
PICCIONE, Paolo
Institución
Resumen
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 nowhere 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 nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.