Generic properties of semi-Riemannian geodesic flows

Author(s)

Renato Ghini Bettiol

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2010-06-24

Examining board members

Paolo Piccione; Leonardo Biliotti; Daniel Victor Tausk

• Advisor: Paolo Piccione

Abstract

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). (AU)

• FAPESP's process: 08/07604-0 - Generic properties of semi-Riemannian geodesic flows
• Grantee: Renato Ghini Bettiol
• Support Opportunities: Scholarships in Brazil - Master