It was conjectured in 1 II] (also in [2]) that mixed foliate CR-submanifolds in a complex hyperbolic space are either complex submanffolds or totally real submanifolds. In this paper we give an affirmative solution to this conjecture.

In this paper, we study warped products of contact skew-CR submanifolds, called skew CR-warped products. We establish a lower bound relationship between the squared norm second fundamental form and warping function. The equality case inequality is investigated some special cases derived are given. Furthermore, provide non-trivial examples such submanifolds.

in this paper we consider contact cr-warped product submanifolds of the type $m = n_ttimes_f n_perp$, of a nearly kenmotsu generalized sasakian space form $bar m(f_1‎, ‎f_2‎, ‎f_3)$ and by use of hopf's lemma we show that $m$ is simply contact cr-product under certain condition‎. ‎finally‎, ‎we establish a sharp inequality for squared norm of the second fundamental form and equality case i...

Warped product manifolds provide excellent setting to model space-time near black holes or bodies with large gravitational force (cf. [1], [2], [14]). Recently, results are published exploring the existence (or non-existence) of warped product submanifolds in Kaehlerian and contact settings (cf. [6], [17], [20]). To continue the sequel, we have considered warped product submanifolds of nearly K...

The Riemannian submersions of a CR-hypersurface M of a Kaehler-Einstein man-ifold˜M are studied. If M is an extrinsic CR-hypersurface of˜M, then it is shown that the base space of the submersion is also a Kaehler-Einstein manifold. 1. Introduction. The study of the Riemannian submersions π : M → B was initiated by O'Neill [14] and Gray [9]. This theory was very much developed in the last thirty...

In this paper we consider contact CR-warped product submanifolds of the type $M = N_Ttimes_f N_perp$, of a nearly Kenmotsu generalized Sasakian space form $bar M(f_1‎, ‎f_2‎, ‎f_3)$ and by use of Hopf's Lemma we show that $M$ is simply contact CR-product under certain condition‎. ‎Finally‎, ‎we establish a sharp inequality for squared norm of the second fundamental form and equality case is dis...

In this paper, we discuss submersion of CR-submanifolds of locally conformal Kaehler manifold. We prove that if π : M −→ B◦ is a submersion of CR-submanifold M of a locally conformal Kaehler manifoldM onto an almost Hermitian manifold B◦, then B◦ is a locally conformal Kaehler manifold. Furthermore, we discuss totally umbilical CR-submanifold and cohomology of CR-submanifold of locally conforma...