准齐次三维实解析洛仑兹度规不存在
Quasihomogeneous three-dimensional real analytic Lorentz metrics do not exist
摘要：
本文证明了${\bf R}^3$上的一个实解析Lorentz度量的芽在其闭包中含有原点的开集上是局部齐次的，它必然是局部齐次的.我们分类李代数，可以准齐次作用-这意味着他们的行动传递的开集承认在其封闭的起源，但不是在起源-和isometrically为这样一个度量。在拟齐次作用量原点的各向同性是半单的情况下，我们给出了度量和作用量的一组完备的标准形。
英文摘要：
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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