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In this paper, we prove two optimal inequalities involving the intrinsic scalar curvature and extrinsic Casorati curvature of submanifolds of generalized space forms endowed with a semi-symmetric metric connection. Moreover, we also characterize those submanifolds for which the equality cases hold.

OPTIMAL INEQUALITIES FOR THE CASORATI CURVATURES OF SUBMANIFOLDS OF GENERALIZED SPACE FORMS ENDOWED WITH SEMI-SYMMETRIC METRIC CONNECTIONS