Abstract:

In this paper, we obtained a geometric inequality for doubly warped product submanifolds in a Riemannian manifold of nearly quasiconstant curvature by using algebraic lemma and fundamental equations. We also established an inequality involving Ricci curvature and mean curvature, and discussed the equality conditions of the inequalities.

Key words: inequality, submanifold, Riemannian manifold of nearly quasiconstant curvature, doubly warped product