On the local and global properties of geodesics in pseudo-Riemannian metrics

Autor(es)

Remizov, A. O. ^[1]

Afiliação do(s) autor(es)

^[1] Ecole Polytech, CNRS, CMAP, F-91128 Palaiseau - France

• Tipo de documento: Artigo Científico
• Fonte: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS; v. 39, p. 36-58, APR 2015.
• Citações Web of Science: 3

Resumo

The paper is a study of geodesics in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investigated. The equation of the geodesic flow has singularities at such points that leads to a curious phenomenon: geodesics cannot pass through such a point in arbitrary tangential directions, but only in certain directions said to be admissible (the number of admissible directions is generically 1 or 3). Secondly, we study the global properties of geodesics in pseudo-Riemannian metrics possessing differentiable groups of symmetries. At the end of the paper, two special types of discontinuous metrics are considered. (C) 2015 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 12/03960-2 - Geodésicas em superfícies com métricas singulares
• Beneficiário: Farid Tari
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional