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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Piecewise Euclidean structures and Eberlein's Rigidity Theorem in the singular case

Michael W Davis, Boris Okun and Fangyang Zheng

Geometry & Topology 3 (1999) 303–330

arXiv: math.GT/9812011

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.

Keywords
piecewise Euclidean structure, CAT(0) space, Hadamard space, rigidity theorem
Mathematical Subject Classification
Primary: 57S30
Secondary: 53C20
References
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Publication
Received: 19 December 1998
Accepted: 27 August 1999
Published: 13 September 1999
Proposed: Steve Ferry
Seconded: Walter Neumann, David Gabai
Authors
Michael W Davis
Department of Mathematics
The Ohio State University
Columbus
Ohio 43201
USA
Boris Okun
Department of Mathematics
Vanderbilt University
Nashville
Tennessee 37400
USA
Fangyang Zheng
Department of Mathematics
The Ohio State University
Columbus
Ohio 43201
USA