2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79181In 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.htmlGeometric TopologyDifferential Geometry57S30, 53C20text