Piecewise Euclidean structures and Eberlein's Rigidity Theorem in the singular case
Geometric Topology
2007-05-23 v1 Differential Geometry
Abstract
In this article, we generalize Eberlein's Rigidity Theorem to the singular case, namely, one of the spaces is only assumed to be a CAT(0) topological manifold. As a corollary, we get that any compact irreducible but locally reducible locally symmetric space of noncompact type does not admit a nonpositively curved (in the Aleksandrov sense) piecewise Euclidean structure. Any hyperbolic manifold, on the other hand, does admit such a structure.
Cite
@article{arxiv.math/9909191,
title = {Piecewise Euclidean structures and Eberlein's Rigidity Theorem in the singular case},
author = {Michael W. Davis and Boris Okun and Fangyang Zheng},
journal= {arXiv preprint arXiv:math/9909191},
year = {2007}
}
Comments
28 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper13.abs.html