In this paper we study the geodesic connectedness of some open connected subsets (regions) of a Lorentzian manifold, using a convexity property of the boundary of such regions. Necessary and sufficient conditions on the metric are given for the convexity of the boundary of such regions. Finally it is presented a result on the geodesic connectedeness of the whole manifold which relates the asymptotic behaviour of the coefficients of the metric to the convexity of the boundary of a family of regions which cover the manifold.
Convex regions of Lorentzian manifolds / Masiello, Antonio. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 167:1(1994), pp. 299-322. [10.1007/BF01760337]
Convex regions of Lorentzian manifolds
Antonio Masiello
1994-01-01
Abstract
In this paper we study the geodesic connectedness of some open connected subsets (regions) of a Lorentzian manifold, using a convexity property of the boundary of such regions. Necessary and sufficient conditions on the metric are given for the convexity of the boundary of such regions. Finally it is presented a result on the geodesic connectedeness of the whole manifold which relates the asymptotic behaviour of the coefficients of the metric to the convexity of the boundary of a family of regions which cover the manifold.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
