Generic properties of semi-Riemannian geodesic flows

Details Generic properties of semi-Riemannian geodesic flows Generic properties of semi-Riemannian geodesic flows

2010-08-30

arxiv.org/abs/1008.4986v1

Mathematics

Differential Geometry

248 pages, 33 figures, MSc. dissertation

Scientific paper

Let M be a possibly non compact smooth manifold. We study genericity in the C^k-topology (3<=k<=+infty) of nondegeneracy properties of semi-Riemannian geodesic flows on M. Namely, we prove a new version of the Bumpy Metric Theorem for a such M and also genericity of metrics that do not possess any degenerate geodesics satisfying suitable endpoints conditions. This extends results in the literature for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P of MxM that satisfies an admissibility condition. Immediate consequences are generic non conjugacy between two points and non focality between a point and a submanifold (or also between two submanifolds).

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