Nonpositively curved manifolds containing a prescribed nonpositively   curved hypersurface
  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. 
T. Tam Nguyen Phan
math.DG