Genericity of nondegenerate critical points and Morse geodesic functionals

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Based on an idea of B. White, we prove an abstract genericity result that employs the infinite dimensional Sard--Smale theorem. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.
23 pages; a new section (now number 5) about genericity in the C^\infty-topology has been added and other minor changes

Keywords

Differential Geometry, Functional Analysis, 57R45, 57R70, 57N75, 58E10

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/208476

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0804.3724
 http://arxiv.org/abs/0804.3724

Collections

arXiv