The present paper deals with a study of warped product submanifolds of (LCS)n-manifolds and warped product semi-slant submanifolds of (LCS)n-manifolds. It is shown that there exists no proper warpedâ€¦ (More)

The geometry of manifolds endowed with geometrical structures has been intensively studied, and several important results have been published. In this paper, we deal with manifolds having aâ€¦ (More)

We show that there exist no proper warped product semi-invariant submanifolds in almost paracontact Riemannian manifolds such that totally geodesic submanifold and totally umbilical submanifold ofâ€¦ (More)

In this paper, the geometry of F -invariant CR-submanifolds of a Kaehlerian product manifold is studied. Fundamental properties of this type submanifolds are investigated such as CR-product,â€¦ (More)

In this chapter, we introduce the theory of sub-manifolds of a Riemannian manifold. The fundamental notations are given. The theory of sub-manifolds of an almost Riemannian product manifold is one ofâ€¦ (More)

In this paper, the geometry of invariant submanifolds of a Sasakian manifold are studied. Necessary and sufficient conditions are given on an submanifold of a Sasakian manifold to be invariantâ€¦ (More)

The object of the present paper is to study generalized Sasakianspace-forms with the conditions satisfying CÌƒ(Î¾,X)CÌƒ = 0, CÌƒ(Î¾,X)R = 0, CÌƒ(Î¾,X)S = 0 and CÌƒ(Î¾,X)P = 0. According these cases,â€¦ (More)

and Applied Analysis 3 aR (X, Y) Î¾ + b [S (Y, Î¾)X âˆ’ S (X, Î¾) Y +g (Y, Î¾) QX âˆ’ g (X, Î¾) QY] âˆ’ Ï„ n [ a n âˆ’ 1 + 2b] [g (Y, Î¾)X âˆ’ g (X, Î¾) Y] = 0. (24) Here, taking into account of (16), we have [Î· (Y)Xâ€¦ (More)

In this article we investigate the geometry of CR-lightlike submanifolds in an indefinite KÃ¤hler product manifold. In particular, we obtain the necessary and sufficient conditions for a CR-lightlikeâ€¦ (More)