On the infinitesimal orbit type of maximal dimensional orbits
| Autor: | D. Szeghy |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Pure mathematics
Dense set Mathematical analysis Lie group Stable manifold theorem Type (model theory) Pseudo-Riemannian manifold Manifold symbols.namesake Computational Theory and Mathematics Orbit (dynamics) symbols Mathematics::Differential Geometry Geometry and Topology Invariant (mathematics) Analysis Mathematics |
| Zdroj: | Differential Geometry and its Applications. 35:86-105 |
| ISSN: | 0926-2245 |
| DOI: | 10.1016/j.difgeo.2014.04.013 |
| Popis: | We prove that in the case of an isometric action α : G × M → M of a Lie group G on a semi-Riemannian manifold M the union of the maximal dimensional orbits is an open and dense set in M. Moreover, if M is a Lorentz manifold and α is an isometric action on it, then in the set of the maximal dimensional orbits local stability and normalizability are equivalent, and there is no open invariant set U ⊂ M such that all the orbits G ( x ) ⊂ U are non-normalizable and have the same infinitesimal type. These results are useful in the extension of the principal orbit type theorem. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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