If M is a Riemannian manifold with $Ric \ge  \left( {n  1} \right)$, $$ds_M^2 = d{t^2} + \exp \left( {2t} \right)ds_N^2$$ N is a submanifold of M. Then by Gaussequation, we can prove $Ric\left( N \right) \ge 0$. If M is an Alexandrov space with $Ric \ge  \left( {n  1} \right)$ (or $\sec \ge  1$) and a warped product like above. Can we get similar information about N?
