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Geodesics in the sub-Lorentzian geometry

Grochowski M.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 2

161-178

The aim of this paper is to introduce the notion of sub-Lorentzian manifolds (which is done by analogy to sub-Riemannian manifolds) and to describe basic properties of such manifolds. In particular, we investigate problems related to the existence of the longest curves between two given points, and examine some conditions for continuity and differentiability of the (local) sub-Lorentzian distance function.