On Optimal Casorati Inequalities for $PTR$-Submanifolds of Complex Space Forms
Abstract
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.
Keywords
References
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Details
Primary Language
English
Subjects
Algebraic and Differential Geometry
Journal Section
Research Article
Authors
Gülistan Polat
0000-0002-5798-7796
Türkiye
Ramazan Demir
*
0000-0001-9476-3823
Türkiye
Sema Kazan
0000-0002-8771-9506
Türkiye
Cumali Yıldırım
0000-0002-2073-4752
Türkiye
Publication Date
June 30, 2026
Submission Date
March 23, 2026
Acceptance Date
June 29, 2026
Published in Issue
Year 2026 Number: 55