DOI: 10.53570/jnt.1914322 ISSN: 2149-1402

On Optimal Casorati Inequalities for $PTR$-Submanifolds of Complex Space Forms

Gülistan Polat, Ramazan Demir, Sema Kazan, Cumali Yıldırım
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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 $\delta$-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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