Some relationships between intrinsic and extrinsic invariants of submanifolds in generalized $S$-space-forms

We establish some inequalities of Chen’s type between certain intrinsic invariants insert ignore into journalissuearticles values(involving sectional, Ricci and scalar curvatures); and the squared mean curvature of submanifolds tangent to the structure vector fields of a generalized $S$-space-form and we discuss the equality cases of them. We apply the obtained results to slant submanifolds.