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In this paper we give a new proof for two sharp inequalities involving generalized normalized δ-Casorati curvatures of a slant submanifold in a quaternionic space form. These inequalities were recently obtained in Lee and Vîlcu (Taiwan. J. Math. 19(3):691-702, 2015) using an optimization procedure by showing that a quadratic polynomial in the components of the second fundamental form is parabolic. The new proof is obtained analyzing a suitable constrained extremum problem on submanifold.
Lee et al. (Mon,) studied this question.