Generic properties of semi-Riemannian geodesic flows

• Ano de defesa: 2010
• Autor(a) principal: Bettiol, Renato Ghini
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Bumpy Metric Theorem; condições de pontos finais generalizadas; fluxos geodésicos; general endpoints conditions; generic properties; geodesic flows; propriedades genéricas; semi-Riemannian manifolds; Teorema de Métricas Bumpy; variedades semi-Riemannianas
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-21072010-170243/

Let M be a possibly non compact smooth manifold. We study genericity in the C^k topology (3<=k<=+infty) of nondegeneracy properties of semi-Riemannian geodesic flows on M. Namely, we prove a new version of the Bumpy Metric Theorem for a such M and also genericity of metrics that do not possess any degenerate geodesics satisfying suitable endpoints conditions. This extends results of Biliotti, Javaloyes and Piccione for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P of MxM that satisfies an admissibility condition. Immediate consequences are generic non conjugacy between two points and non focality between a point and a submanifold (or also between two submanifolds).