Remarks on Chen’s Inequalities for Submanifolds of a Riemannian Manifold of Nearly Quasi-Constant Curvature

Abstract

In this paper, we prove Chen’s general inequalities and Chen–Ricci inequalities for submanifolds of a Riemannian manifold of nearly quasi-constant curvature. We also establish inequalities between the warping function and the squared mean curvature for warped product submanifolds in a Riemannian manifold of nearly quasi-constant curvature.