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 $M$...

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

We obtain on a Kähler B-manifold (i.e., manifold with Norden metric) some corresponding results from the Kählerian and para-Kählerian context concerning Bochner curvature. prove that such is of constant totally real sectional curvatures if only it holomorphic Einstein, flat manifold. Moreover, we provide necessary sufficient conditions for gradient Ricci soliton or ?-Einstein metric to be flat....

In this article we obtain the pinching of the null sectional curvature of CRlightlike submanifolds of an inde…nite Hermitian manifold. As a result of this inequality we conclude some non-existence results of such lightlike submanifolds.Moreover using the Index form we prove more non-existence results for CR-lightlike submanifolds. 1. Introduction The theory of submanifolds of a Riemannian or se...

In this paper, we establish the following result: Let M be an n-dimensional complete totally real minimal submanifold immersed in CPn with Ricci curvature bounded from below. Then either M is totally geodesic or infr ≤ (3n+1)(n−2)/3, where r is the scalar curvature of M .

In this article, we study the smoothness of Riemannian submersions for open manifolds with non-negative sectional curvature. Suppose thatM is a C-smooth, complete and non-compact Riemannian manifold with nonnegative sectional curvature. Cheeger-Gromoll [ChG] established a fundamental theory for such a manifold. Among other things, they showed that M admits a totally convex exhaustion {Ωu}u≥0 of...

We derive and study necessary and sufficient conditions for an S-bundle to admit an invariant metric of positive or nonnegative sectional curvature. In case the total space has an invariant metric of nonnegative curvature and the base space is odd dimensional, we prove that the total space contains a flat totally geodesic immersed cylinder. We provide several examples, including a connection me...