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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.

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