Quasihomogeneous three-dimensional real analytic Lorentz metrics do not exist
Abstract
We show that a germ of a real analytic Lorentz metric on which is locally homogeneous on an open set containing the origin in its closure is necessarily locally homogeneous. We classifiy Lie algebras that can act quasihomogeneously---meaning they act transitively on an open set admitting the origin in its closure, but not at the origin---and isometrically for such a metric. In the case that the isotropy at the origin of a quasihomogeneous action is semisimple, we provide a complete set of normal forms of the metric and the action.
Keywords
Cite
@article{arxiv.1406.2302,
title = {Quasihomogeneous three-dimensional real analytic Lorentz metrics do not exist},
author = {Sorin Dumitrescu and Karin Melnick},
journal= {arXiv preprint arXiv:1406.2302},
year = {2015}
}
Comments
23 pp. Took the place of "Quasihomogeneous three-dimensional real analytic Lorentz metrics" (arXiv:1401.6272), which was withdrawn by the first author. Revised version incorporates several minor corrections, including those suggested by the referee