arXiv math/99091911999-09-13math.GTmath.DG

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

Michael W. Davis, Boris Okun, Fangyang Zheng

备注：: 28 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper13.abs.html
发表信息：: Geom. Topol. 3 (1999), 303-330

英文摘要：

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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