TOPOLOGICAL AND DIFFERENTIABLE SPHERE THEOREMS FOR 4− DIMENSIONAL CR-WARPED PRODUCT SUBMANIFOLDS OF 6-DIMENSIONAL UNIT SPHERE

Abstract

In this paper, taking into account that the 6-dimensional unit sphere is nearly
Kaehler manifold, 4-dimensional CR-warped product submanifolds of the sphere are studied.
First, an interesting relation is obtained among the warping function of the CR-warped product submanifold, the scalar curvature of the fibers and the components of the second fundamental form.Using this relation, topological and differential sphere theorems are given and totally geodesicity of CR-warped product submanifold of the 6-dimensional sphere is obtained. Moreover, a result is presented about homology groups of a CR-warped submanifold.