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.
1994
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/10493
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