Quasihomogeneous Three-dimensional Real Analytic Lorentz Metrics Do Not Exist
نویسندگان
چکیده
We show that a germ of a real analytic Lorentz metric on R3 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 semi-simple, we provide a complete set of normal forms of the metric and the action.
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