Nonpositively curved manifolds containing a prescribed nonpositively curved hypersurface

Abstract

We use pinched smooth hyperbolization to show that every closed, nonpositively curved $n$-dimensional manifold $M$ can be embedded as a totally geodesic submanifold of a closed, nonpositively curved $(n+1)$-dimensional manifold $\hat{M}$ of geometric rank one.

2 pages, to appear in the Topology Proceedings of the 2012 Spring Topology $ Dynamics Conference