In this paper we prove two sharp inequalities involving the normalized scalar curvature and the generalized normalized δ-Casorati curvatures for slant submanifolds in quaternionic space forms. We also characterize those submanifolds for which the equality cases hold. These results are a generalization of some recent results concerning the Casorati curvature for a slant submanifold in a quaterni...

In this paper, we study pseudo-slant submanifolds of nearly Kaehler manifolds. A classification theorem on a totally umbilical pseudo-slant submanifold of a nearly Kaehler manifold is proved. 2000 Mathematics Subject Classification: 53C40, 53B25, 53C15.

We study GCR-lightlike submanifolds of semi-Riemannian product manifolds. give some equivalent conditions for the integrability various distributions manifolds and investigate geometry leaves distributions.

In this paper, we study warped product pseudo-slant submanifolds of nearly Kaehler manifolds. We prove the non-existence results on warped product submanifolds of a nearly Kaehler manifold.

Our paper aims to study the geometry of submanifolds an almost-complex metallic manifold. We give example this type manifold, and reveal fundamental properties structure induced on submanifolds. establish subsets in manifolds, such as invariant, anti-invariant, slant

We study some properties of a half-lightlike submanifoldM , of a semi-Riemannianmanifold, whose shape operator is conformal to the shape operator of its screen distribution. We show that any screen distribution S(TM) of M is integrable and the geometry of M has a close relation with the nondegenerate geometry of a leaf of S(TM). We prove some results on symmetric induced Ricci tensor and null s...

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we study the geometry of a semi-Riemannian manifold ¯ M of quasi-constant curvature. The main result is two characterization theorems for ¯ M admits solenoidal and screen totally umbilical r (> 1)-lightlike subm...