GT Vol 3 (1999) Paper 13 (Abstract)

Geometry & Topology, Vol. 3 (1999) Paper no. 13, pages 303--330.

Piecewise Euclidean Structures and Eberlein's Rigidity Theorem in the Singular Case

Michael W Davis, Boris Okun, Fangyang Zheng

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

AMS subject classification. Primary: 57S30. Secondary: 53C20.

DOI: 10.2140/gt.1999.3.303

E-print: arXiv:math.GT/9909191

Submitted to GT on 19 December 1998. Paper accepted 27 August 1999. Paper published 13 September 1999.

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Michael W Davis, Boris Okun, Fangyang Zheng

Department of Mathematics, The Ohio State University
Columbus, OH 43201, USA

Department of Mathematics, Vanderbilt University
Nashville, TN 37400, USA

Department of Mathematics, The Ohio State University
Columbus, OH 43201, USA

Email: mdavis@math.ohio-state.edu, okun@math.vanderbilt.edu, zheng@math.ohio-state.edu

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