We prove the semi-Riemannian bumpy metric theorem using equivariant variational genericity. The theorem states that, on a given compact manifold M, the set of semi-Riemannian metrics that admit only nondegenerate closed geodesics is generic relatively to the Ck-topology, k = 2, . . . ,∞, in the set of metrics of a given index on M. A higher-order genericity Riemannian result of Klingenberg and Takens is extended to semi-Riemannian geometry
On the semi-Riemannian bumpy metric theorem / Biliotti, Leonardo; JAVALOYES MIGUEL, Angel; Piccione, Paolo. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 84:1(2011), pp. 1-18.
On the semi-Riemannian bumpy metric theorem.
BILIOTTI, Leonardo;
2011-01-01
Abstract
We prove the semi-Riemannian bumpy metric theorem using equivariant variational genericity. The theorem states that, on a given compact manifold M, the set of semi-Riemannian metrics that admit only nondegenerate closed geodesics is generic relatively to the Ck-topology, k = 2, . . . ,∞, in the set of metrics of a given index on M. A higher-order genericity Riemannian result of Klingenberg and Takens is extended to semi-Riemannian geometry| File | Dimensione | Formato | |
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