A lower bound for the Ricci curvature of submanifolds in generalized Sasakian space forms

In this paper, we obtain inequalities between the Ricci curvature, the scalar curvature and the squared mean curvature of submanifolds in generalized Sasakian space forms such that each inequality is a lower bound for the Ricci curvature. Also, we obtain a sharp relationship between the scalar curvature, a Riemannian invariant and the squared mean curvature of anti-invariant submanifolds in generalized Sasakian space forms.