Optimal inequalities for the Casorati curvatures of submanifolds of real space forms endowed with semi-symmetric metric connections

In this paper, we prove two optimal inequalities involving the intrinsic scalar curvature and extrinsic Casorati curvature of submanifolds of real space forms endowed with a semi-symmetric metric connection. Moreover, we show that in both cases, the equality at all points characterizes the invariantly quasi-umbilical submanifolds. MSC: 53C40, 53B05.