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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
