On the semi-Riemannian bumpy metric theorem

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 C(k)-topology, k=2, ..., infinity, 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.

MIUR

M.I.U.R.

GNSAGA of INdAM

GNSAGA of INdAM

Regional Junta Andalucia

Regional Junta Andalucia[P09-FQM-4496]

MICINN[MTM2009-10418]

MICINN

Fundacion Seneca[04540/GERM/06]

Fundacion Seneca

Excellence Groups of the Region de Murcia, Spain

Excellence Groups of the Region de Murcia, Spain

Regional Agency for Science and Technology

Regional Agency for Science and Technology

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Capes, Brasil[BEX 1509-08-0]

Fundacion Seneca, Spain[09708/IV2/08]

Fundacion Seneca, Spain