Orthogonal geodesics in manifolds with singular boundary. Applications to the theo...
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Univ Sao Paulo, Dept Matemat, BR-05508090 Sao Paulo - Brazil
[2] Univ Camerino, Dipartimento Matemat & Informat, I-62032 Camerino - Italy
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 35, n. 2, p. 339-365, JUN 2010. |
| Web of Science Citations: | 1 |
| Abstract | |
Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), 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 L. Biliotti, M. A. Javaloyes and P. Piccione {[}6] for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P subset of M x M that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal Delta subset of M x M. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C(k)-generic are given. (AU) | |
| FAPESP's process: | 08/07604-0 - Generic properties of semi-Riemannian geodesic flows |
| Grantee: | Renato Ghini Bettiol |
| Support Opportunities: | Scholarships in Brazil - Master |