Bounds of generalized normalized δ-Casorati curvatures for real hypersurfaces in the complex quadric

In the present paper, we first characterize real hypersurfaces in the complex quadric Qmby giving an inequality in terms of the scalar curvature and the Mean curvature vector field. We also obtain the condition under which this inequality becomes an equality. Further, we develop two extremal inequalities involving the normalized delta-Casorati curvatures and the extrinsic generalized normalized delta-Casorati curvatures for real hypersurfaces in Qm. Finally, we derive the necessary and sufficient condition for the equality in both cases.