Flat pseudo-Riemannian homogeneous spaces with non-abelian holonomy group
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- by Oliver Baues and Wolfgang Globke PDF
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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 $\geq 8$, 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.References
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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
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2898710