In this paper we obtain an existence theorem for normal geodesics joining two given submanifolds in a globally hyperbolic stationary spacetime M. The proof is based on both variational and geometric arguments involving the causal structure of M, the completeness of suitable Finsler metrics associated to it and some basic properties of a submersion. By this interaction, unlike previous results on the topic, also non-spacelike submanifolds can be handled.

Normal geodesics connecting two submanifolds in a stationary spacetime

CANDELA, Anna Maria;
2010

Abstract

In this paper we obtain an existence theorem for normal geodesics joining two given submanifolds in a globally hyperbolic stationary spacetime M. The proof is based on both variational and geometric arguments involving the causal structure of M, the completeness of suitable Finsler metrics associated to it and some basic properties of a submersion. By this interaction, unlike previous results on the topic, also non-spacelike submanifolds can be handled.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/13068
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