On doubly warped product submanifolds of Generalized $(κ,μ)$-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.