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

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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.
28 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper13.abs.html

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Geometric Topology, Differential Geometry, 57S30, 53C20

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http://salesiana.dossiersoluciones.com/handle/123456789/79181

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9909191
 http://arxiv.org/abs/math/9909191
 Geom. Topol. 3 (1999), 303-330

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arXiv