Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: October 27, 2011
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53C30, 57S30, 20G05

Retrieve articles in all journals with MSC (2010): 53C30, 57S30, 20G05


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: http://dx.doi.org/10.1090/S0002-9939-2011-11080-3
PII: S 0002-9939(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.