B. Y. Chen inequalities for submanifolds of a Riemannian manifold of quasi-constant curvature

In this paper, we prove B. Y. Chen inequalities for submanifolds of a Riemannian manifold of quasiconstant curvature, i.e., relations between the mean curvature, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered.