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arXiv · 1406.2302

Quasihomogeneous three-dimensional real analytic Lorentz metrics do not exist

Sorin Dumitrescu·Karin Melnick
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Abstract

We show that a germ of a real analytic Lorentz metric on ${\bf R}^3$ 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.

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Sorin Dumitrescu, Karin Melnick. 2014-06-09. Quasihomogeneous three-dimensional real analytic Lorentz metrics do not exist. https://doi.org/10.1007/s10711-015-0078-4

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