Chen-Tripathi Inequality for Warped Product Submanifolds of S-space Forms

Abstract

We obtain Chen-Tripathi inequality (cf. Theorem 2.1) involving the Laplacian of the warping function and the squared mean curvature of warped product integral submanifolds of an S-space form. Then we find obstructions to the existence of minimal isometric immersions of warped product integral submanifolds of S-space forms. In particular, we get corresponding results for C-totally real warped product submanifolds in Sasakian space forms. We also obtain Chen-Tripathi inequality for warped product submanifolds of an S-space form which are tangent to the structure vector fields of the ambient space.