A criterion for the existence of Killing vectors in 3D
General Relativity and Quantum Cosmology
2018-08-08 v1 Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1804.11032,
title = {A criterion for the existence of Killing vectors in 3D},
author = {Boris Kruglikov and Kentaro Tomoda},
journal= {arXiv preprint arXiv:1804.11032},
year = {2018}
}
Comments
24 pages, 5 figures