Flat pseudo-Riemannian homogeneous spaces with non-abelian holonomy group

Authors:
Oliver Baues and Wolfgang Globke

Journal:
Proc. Amer. Math. Soc. **140** (2012), 2479-2488

MSC (2010):
Primary 53C30, 57S30; Secondary 20G05

DOI:
https://doi.org/10.1090/S0002-9939-2011-11080-3

Published electronically:
October 27, 2011

MathSciNet review:
2898710

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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 , 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.

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Additional Information

**Oliver Baues**

Affiliation:
Department of Mathematics, Institute for Algebra and Geometry, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany

Email:
baues@kit.edu

**Wolfgang Globke**

Affiliation:
Department of Mathematics, Institute for Algebra and Geometry, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany

Email:
globke@math.uni-karlsruhe.de

DOI:
https://doi.org/10.1090/S0002-9939-2011-11080-3

Received by editor(s):
October 1, 2010

Received by editor(s) in revised form:
February 16, 2011

Published electronically:
October 27, 2011

Communicated by:
Jianguo Cao

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.