On Hypersurfaces of Hessian Manifolds with Constant Hessian Sectional Curvature

integral inequalities for submanifolds of hessian manifolds with constant hessian sectional curvature

in this paper, we obtain two intrinsic integral inequalities of hessian manifolds.

Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian

We introduce various families of irreducible homaloidal hypersurfaces in projective space Pr, for all r ≥ 3. Some of these are families of homaloidal hypersurfaces whose degrees are arbitrarily large as compared to the dimension of the ambient projective space. The existence of such a family solves a question that has naturally arisen from the consideration of the classes of homaloidal hypersur...

Constant k-curvature hypersurfaces in Riemannian manifolds

In [8], Rugang Ye proved the existence of a family of constant mean curvature hypersurfaces in an m+ 1-dimensional Riemannian manifold (M, g), which concentrate at a point p0 (which is required to be a nondegenerate critical point of the scalar curvature), moreover he proved that this family constitute a foliation of a neighborhood of p0. In this paper we extend this result to the other curvatu...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Totally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures

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 $M$...