Generic properties of semi-Riemannian geodesic flows

2010/08/30 by Renato G. Bettiol, Bettiol, Renato G.
Mathematics · #53C50 #57N75 #58Exx #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Morphological variations and asymmetry #math.DG #math.DS #msc:53C50 #msc:57N75 #msc:58Exx

paper · pdf · doi:10.48550/arxiv.1008.4986

248 pages, 33 figures, MSc. dissertation

arxiv created 2010/08/30 · openalex publication_date 2010/08/30 · arxiv updated 2010/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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