Holonomy Groups of Complete Flat PseudoRiemannian Homogeneous Spaces
Abstract
We show that a complete flat pseudoRiemannian homogeneous manifold with nonabelian linear holonomy is of dimension at least 14. Due to an example constructed in a previous article by Oliver Baues and the author, this is a sharp bound. Also, we give a structure theory for the fundamental groups of complete flat pseudoRiemannian manifolds in dimensions less than 7. Finally, we observe that every finitely generated torsionfree 2step nilpotent group can be realized as the fundamental group of a complete flat pseudoRiemannian manifold with abelian linear holonomy.
 Publication:

arXiv eprints
 Pub Date:
 May 2012
 arXiv:
 arXiv:1205.3285
 Bibcode:
 2012arXiv1205.3285G
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics;
 Mathematics  Group Theory;
 53C30;
 57S30;
 20G05
 EPrint:
 16 pages