Piecewise Euclidean structures and Eberlein's Rigidity Theorem in the singular case

Michael W. Davis; Boris Okun; Fangyang Zheng

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arXiv · math/9909191

Piecewise Euclidean structures and Eberlein's Rigidity Theorem in the singular case

Michael W. Davis·Boris Okun·Fangyang Zheng

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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.

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Michael W. Davis, Boris Okun, Fangyang Zheng. 1999-09-13. Piecewise Euclidean structures and Eberlein's Rigidity Theorem in the singular case. https://arxiv.org/abs/math/9909191

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