In this paper we characterize the convexity of the boundary aS of a static (standard) Lorentzian manifold S in terms of Jacobi metrics. From this result, we also obtain: (1) a characterization of the convexity of aS computable from its "spacelike" part, (2) the equivalence between the variational and geometrical definitions of convexity for aS, and (3) a very precise result on existence of geodesics joining a point and a line on S.
A note on the boundary of a static Lorentzian manifold / Bartolo, R; Germinario, A; Sánchez, M. - In: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS. - ISSN 0926-2245. - STAMPA. - 16:2(2002), pp. 121-131. [10.1016/S0926-2245(02)00062-1]
A note on the boundary of a static Lorentzian manifold
Bartolo R;
2002-01-01
Abstract
In this paper we characterize the convexity of the boundary aS of a static (standard) Lorentzian manifold S in terms of Jacobi metrics. From this result, we also obtain: (1) a characterization of the convexity of aS computable from its "spacelike" part, (2) the equivalence between the variational and geometrical definitions of convexity for aS, and (3) a very precise result on existence of geodesics joining a point and a line on S.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
