# On the semi-Riemannian bumpy metric theorem - Mathematics > Differential Geometry

Abstract: We prove the semi-Riemannian bumpy metric theorem using equivariantvariational genericity. The theorem states that, on a given compact manifold$M$, the set of semi-Riemannian metrics that admit only nondegenerate closedgeodesics is generic relatively to the $C^k$-topology, $k=2, .,\infty$, in theset of metrics of a given index on $M$. A higher order genericity Riemannianresult of Klingenberg and Takens is extended to semi-Riemannian geometry.

Author: Leonardo Biliotti, Miguel Angel Javaloyes, Paolo Piccione

Source: https://arxiv.org/