A criterion for the existence of Killing vectors in 3D
| Autor: | Kentaro Tomoda, Boris Kruglikov |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Physics
Mathematics - Differential Geometry Pure mathematics Physics and Astronomy (miscellaneous) 010308 nuclear & particles physics Infinitesimal Scalar (mathematics) FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) Riemannian manifold Curvature 01 natural sciences General Relativity and Quantum Cosmology Differential Geometry (math.DG) 0103 physical sciences FOS: Mathematics Mathematics::Differential Geometry 010306 general physics |
| DOI: | 10.48550/arxiv.1804.11032 |
| Popis: | A three-dimensional Riemannian manifold has locally 6, 4, 3, 2, 1 or none independent Killing vectors. We present an explicit algorithm for computing dimension of the infinitesimal isometry algebra. It branches according to the values of curvature invariants. These are relative differential invariants computed via curvature, but they are not scalar polynomial Weyl invariants. We compare our obstructions to the existence of Killing vectors with the known existence criteria due to Singer, Kerr and others. Comment: 24 pages, 5 figures |
| Databáze: | OpenAIRE |
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