LAUSR

In the present paper, we first characterize real hypersurfaces in the complex quadric $$Q^{m}$$Qm by 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 $$\delta $$δ-Casorati curvatures and the extrinsic generalized normalized $$\delta $$δ-Casorati curvatures for real hypersurfaces in $$Q^{m}$$Qm. Finally, we derive the necessary and sufficient condition for the equality in both cases.