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Mathematics > Differential Geometry

arXiv:1406.2302 (math)
[Submitted on 9 Jun 2014 (v1), last revised 25 May 2015 (this version, v2)]

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

Authors: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.
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 Took the place of "Quasihomogeneous three-dimensional real analytic Lorentz metrics" (arXiv:1401.6272), which was withdrawn by the first author.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
Subjects: Differential Geometry (math.DG)
MSC classes: 53A55, 53B30, 53C50
Cite as: arXiv:1406.2302 [math.DG]
  (or arXiv:1406.2302v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1406.2302
Related DOI: https://doi.org/10.1007/s10711-015-0078-4

Submission history

From: Karin Melnick [view email]
[v1] Mon, 9 Jun 2014 19:55:46 UTC (28 KB)
[v2] Mon, 25 May 2015 15:39:36 UTC (30 KB)
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