Abstract
By optimization methods on Riemannian submanifolds, we establish two inequalities between the intrinsic and extrinsic invariants, for generalized normalized <i>δ</i>-Casorati curvatures of warped product submanifolds in a Riemannian manifold of quasi-constant curvature. We generalize the conclusions of the optimal inequalities of submanifolds in real space forms.
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