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arXiv · 0910.4175

Genericity of nondegenerate geodesics with general boundary conditions

Renato G. Bettiol·Roberto Giambò
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Abstract

Let M be a possibly noncompact manifold. We prove, generically in the C^k-topology (k=2,...,\infty), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of Biliotti, Javaloyes and Piccione for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P of the product MxM that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal of MxM. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C^k-generic are given.

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Renato G. Bettiol, Roberto Giambò. 2009-10-21. Genericity of nondegenerate geodesics with general boundary conditions. https://arxiv.org/abs/0910.4175

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