Holonomy Groups of Complete Flat Pseudo-Riemannian Homogeneous Spaces

Abstract

We show that a complete flat pseudo-Riemannian homogeneous manifold with non-abelian 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 pseudo-Riemannian manifolds in dimensions less than 7. Finally, we observe that every finitely generated torsion-free 2-step nilpotent group can be realized as the fundamental group of a complete flat pseudo-Riemannian manifold with abelian linear holonomy.

16 pages

References in corpus (2)

• Prehomogeneous Affine Representations and Flat Pseudo-Riemannian Manifolds
• Flat Pseudo-Riemannian Homogeneous Spaces with Non-Abelian Holonomy Group

Cited by in corpus (1)

• On the Geometry of Flat Pseudo-Riemannian Homogeneous Spaces