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.
Citation
Michael W Davis. Boris Okun. Fangyang Zheng. "Piecewise Euclidean structures and Eberlein's Rigidity Theorem in the singular case." Geom. Topol. 3 (1) 303 - 330, 1999. https://doi.org/10.2140/gt.1999.3.303
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