Abstract
The purpose of this paper is to consider the geometry of a manifold M, equipped with an arbitrary symmetric (0,2) tensor field g. If this tensor field has singular points, i.e. points where g degenerates, then the pair ( M, g) is called a singular semi Riemannian manifold. In this paper we prove an existence theorem for geodesics through singular points and parallel translate along smooth curves through singular points. Furthermore we prove existence and uniqueness of geodesics, parallel frames and Jacobi fields along geodesics for conformal singular points. Finally it is proven that repeated zeroes of Jacobi fields along geodesics through conformal singular points retain their significance as an almost meeting point for nearby geodesics.
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