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Type: Journal article
Title: Rigidity of compact pseudo-Riemannian homogeneous spaces for solvable Lie groups
Author: Baues, O.
Globke, W.
Citation: International Mathematics Research Notices, 2017; 2018(10):3199-3223
Publisher: Oxford University Press
Issue Date: 2017
ISSN: 1073-7928
Statement of
Oliver Baues and Wolfgang Globke
Abstract: Let M be a compact connected pseudo-Riemannian manifold on which a solvable connected Lie group G of isometries acts transitively. We show that G acts almost freely on M and that the metric onM is induced by a bi-invariant pseudo-Riemannian metric on G. Furthermore, we show that the identity component of the isometry group ofM coincides with G. The proofs rely on a combination of density properties for uniform subgroups of solvable Lie groups and the reduction theory of pseudo-Riemannian metric Lie groups.
Keywords: math.DG
Description: Advance Access Publication February 4, 2017
Rights: © The Author(s) 2017. Published by Oxford University Press. All rights reserved.
RMID: 0030074241
DOI: 10.1093/imrn/rnw320
Grant ID:
Appears in Collections:Mathematical Sciences publications

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