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Investigation establishes sharp inequalities relating curvature properties in PTR submanifolds, highlighting geometric interpretations.
In this paper, we investigate partially totally real ($PTR$) submanifolds of complex space forms and establish two sharp inequalities involving the normalized scalar curvature and the generalized normalized δ-Casorati curvatures. By using the orthogonal decomposition of the tangent bundle induced by the $PTR$ structure and applying the Gauss equation, we derive optimal Casorati-type inequalities. Moreover, we completely characterize the equality cases in terms of invariantly quasi-umbilical submanifolds with a flat normal connection, thereby providing precise geometric interpretations of the results obtained.
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Polat et al. (2026) studied this question.
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