On doubly warped product submanifolds of generalized $$(\kappa ,\mu )$$ ( κ , μ ) -space forms

Abstract

In this paper we establish a general inequality involving the Laplacian of the warping functions and the squared mean curvature of any doubly warped product isometrically immersed in a Riemannian manifold. Moreover, we obtain some geometric inequalities for C-totally real doubly warped product submanifolds of generalized \((\kappa ,\mu )\)-space forms.