Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606001 | Differential Geometry and its Applications | 2015 | 23 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
A.O. Remizov,