Geometriae Dedicata

, Volume 179, Issue 1, pp 229–253 | Cite as

Quasihomogeneous three-dimensional real-analytic Lorentz metrics do not exist

  • Sorin Dumitrescu
  • Karin Melnick
Original Paper


We show that a germ of a real-analytic Lorentz metric on \({\mathbb R}^3\) 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.


Real-analytic Lorentz metrics Transitive Killing Lie algebras  Local differential invariants 

Mathematics Subject Classification (2010)

53A55 53B30 53C50 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Laboratoire J.-A. Dieudonné, UMR 7351Université Côte d’Azur, Université Nice Sophia Antipolis, CNRSNice Cedex 2France
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

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