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A brief survey on singularities of geodesic flows in smooth signature changing metrics on 2-surfacesстатья
- Авторы: Павлова Н.Г., Ремизов А.О.
- Сборник: Advances in Singularities and Foliations: Geometry, Topology and Applications
- Серия: Springer Series in Mathematics and Statistics
- Том: 222
- Глава в коллективной монографии
- Год издания: 2018
- Место издания: Springer International Publishing AG Cham, Switzerland
- Первая страница: 135
- Последняя страница: 155
- DOI: 10.1007/978-3-319-73639-6
- Аннотация: We present a survey on generic singularities of geodesic flows in smooth signature changing metrics (often called pseudo-Riemannian) in dimension 2. Generically, a pseudo-Riemannian metric on a 2-manifold $S$ changes its signature (degenerates) along a curve $S_0$, which locally separates $S$ into a Riemannian ($R$) and a Lorentzian ($L$) domain. The geodesic flow does not have singularities over $R$ and $L$, and for any point $q \in R \cup L$ and every tangential direction $p$ there exists a unique geodesic passing through the point $q$ with the direction $p$. On the contrary, geodesics cannot pass through a point $q \in S_0$ in arbitrary tangential directions, but only in some admissible directions; the number of admissible directions is 1 or 2 or 3. We study this phenomenon and the local properties of geodesics near $q \in S_0$.
- Добавил в систему: Ремизов Алексей Олегович