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.