We show the existence of one spatially closed lightlike geodesic on a regular, conformally stationary Lorentzian manifold M, having a non-contractible, light-convex, timelike cylinder C. The result is obtained by using an extension of the classical Fermat's Principle in optics, proven in [2], and a shortening argument similar to that used in [21] for studying the existence of closed geodesics on Riemannian manifolds with boundary.

Shortening null geodesics in Lorentzian manifolds. Applications to closed light rays / Masiello, A; Piccione, P. - In: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS. - ISSN 0926-2245. - STAMPA. - 8:1(1998), pp. 47-70. [10.1016/S0926-2245(97)00020-X]

Shortening null geodesics in Lorentzian manifolds. Applications to closed light rays

Masiello, A;
1998-01-01

Abstract

We show the existence of one spatially closed lightlike geodesic on a regular, conformally stationary Lorentzian manifold M, having a non-contractible, light-convex, timelike cylinder C. The result is obtained by using an extension of the classical Fermat's Principle in optics, proven in [2], and a shortening argument similar to that used in [21] for studying the existence of closed geodesics on Riemannian manifolds with boundary.
1998
Shortening null geodesics in Lorentzian manifolds. Applications to closed light rays / Masiello, A; Piccione, P. - In: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS. - ISSN 0926-2245. - STAMPA. - 8:1(1998), pp. 47-70. [10.1016/S0926-2245(97)00020-X]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/7935
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