Let V be an open manifold with complete nonnegatively curved metric such that the normal sphere bundle to a soul has no section. We prove that the souls of nearby nonnegatively curved metrics on V are smoothly close. Combining this result with some topological properties of pseudoisotopies we show that for many V the space of complete nonnegatively curved metrics has infinite higher homotopy gr...

Equations on curved manifolds display interesting properties in a number of ways. In particular, the symmetries and, therefore, the conservation laws reduce depending on how curved the manifold is. Of particular interest are the wave and Gordon-type equations; we study the symmetry properties and conservation laws of these equations on the Milne and Bianchi type III metrics. Properties of reduc...

The classical Cartan-Hadamard theorem asserts that a closed Riemannian manifold M with non-positive sectional curvature has universal cover M̃ diffeomorphic to R, and a byproduct of the proof is that ∂∞M̃n is homeomorphic to Sn−1. We prove analogues of these two results in the case where M has a non-empty totally geodesic boundary. More precisely, if M 1 ,M n 2 are two negatively curved Riemannia...

We show that Preissmann’s theorem implies that no closed negatively curved manifold is dominated by a non-trivial product. We also show that a fiber bundle whose base and fiber are negatively curved is dominated by a product if and only if it has a finite covering space which is a trivial bundle.