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Type: Journal article
Title: Flat pseudo-Riemannian homogeneous spaces with non-abelian holonomy group
Author: Baues, O.
Globke, W.
Citation: Proceedings of the American Mathematical Society, 2012; 140(7):2479-2488
Publisher: American Mathematical Society
Issue Date: 2012
ISSN: 0002-9939
Statement of
Oliver Baues and Wolfgang Globke
Abstract: We construct homogeneous flat pseudo-Riemannian manifolds with non-abelian fundamental group. In the compact case, all homogeneous flat pseudo-Riemannian manifolds are complete and have abelian linear holonomy group. To the contrary, we show that there do exist non-compact and non-complete examples, where the linear holonomy is non-abelian, starting in dimensions >/= 8, which is the lowest possible dimension. We also construct a complete flat pseudo-Riemannian homogeneous manifold of dimension 14 with non-abelian linear holonomy. Furthermore, we derive a criterion for the properness of the action of an affine transformation group with transitive centralizer.
Rights: © 2011 American Mathematical Society. Reverts to public domain 28 years from publication
DOI: 10.1090/S0002-9939-2011-11080-3
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Mathematical Sciences publications

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