Submanifold geometry and Morse theory in finite and infinite dimensions
Topics in Lorentzian and Finsler Geometry: geodesic flow and isometry group
| Full text | |
| Author(s): |
Remizov, A. O.
[1]
Total Authors: 1
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| Affiliation: | [1] Ecole Polytech, CNRS, CMAP, F-91128 Palaiseau - France
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS; v. 39, p. 36-58, APR 2015. |
| Web of Science Citations: | 3 |
| Abstract | |
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) | |
| FAPESP's process: | 12/03960-2 - Geodesics on surfaces with singular metrics |
| Grantee: | Farid Tari |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |