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. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard–Smale theorem, along the lines of an analogous result of B. White. 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

Genericity of nondegenerate critical points and Morse geodesic functionals / BILIOTTI L.; MIGUEL ANGEL JAVALOYES; PAOLO PICCIONE. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - 58(2009), pp. 1797-1831.

Genericity of nondegenerate critical points and Morse geodesic functionals

BILIOTTI, Leonardo;
2009

Abstract

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. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard–Smale theorem, along the lines of an analogous result of B. White. 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
Genericity of nondegenerate critical points and Morse geodesic functionals / BILIOTTI L.; MIGUEL ANGEL JAVALOYES; PAOLO PICCIONE. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - 58(2009), pp. 1797-1831.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2286398
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