In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...

We show that H-hypersurfaces of H × R contained in a vertical cylinder and with Ricci curvature with strong quadratic decay have mean curvature |H| > (n − 1)/n. Mathematics Subject Classification: (2000): 53C40, 53C42.

We survey comparison results that assume a bound on the manifold’s Ricci curvature.

In this paper we prove a conjecture by Feldman-IlmanenKnopf in [14] that the gradient shrinking soliton metric they constructed on the tautological line bundle over CP is the uniform limit of blowups of a type I Ricci flow singularity on a closed manifold. We use this result to show that limits of blow-ups of Ricci flow singularities on closed four dimensional manifolds do not necessarily have ...