Research Article

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

Number: 55 June 30, 2026

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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  3. M. Aquib, J. W. Lee, G.-E. Vîlcu, D. W. Yoon, Classification of Casorati ideal Lagrangian submanifolds in complex space forms, Differential Geometry and its Applications 63 (2019) 30–49.
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  6. M. D. Siddiqi, G. Fasihi-Ramandi, M. Hasan, Optimal inequalities for submanifolds in an $({\varepsilon})$-almost para-contact manifolds, Mathematical Analysis and Convex Optimization 2 (1) (2021) 107–118.
  7. M. A. Lone, Inequalities involving Casorati curvatures for submanifolds of real space forms with a quarter-symmetric connection, Filomat 36 (13) (2022) 4483–4491.
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Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Publication Date

June 30, 2026

Submission Date

March 23, 2026

Acceptance Date

June 29, 2026

Published in Issue

Year 2026 Number: 55

APA
Polat, G., Demir, R., Kazan, S., & Yıldırım, C. (2026). On Optimal Casorati Inequalities for $PTR$-Submanifolds of Complex Space Forms. Journal of New Theory, 55, 47-57. https://doi.org/10.53570/jnt.1914322
AMA
1.Polat G, Demir R, Kazan S, Yıldırım C. On Optimal Casorati Inequalities for $PTR$-Submanifolds of Complex Space Forms. JNT. 2026;(55):47-57. doi:10.53570/jnt.1914322
Chicago
Polat, Gülistan, Ramazan Demir, Sema Kazan, and Cumali Yıldırım. 2026. “On Optimal Casorati Inequalities for $PTR$-Submanifolds of Complex Space Forms”. Journal of New Theory, nos. 55: 47-57. https://doi.org/10.53570/jnt.1914322.
EndNote
Polat G, Demir R, Kazan S, Yıldırım C (June 1, 2026) On Optimal Casorati Inequalities for $PTR$-Submanifolds of Complex Space Forms. Journal of New Theory 55 47–57.
IEEE
[1]G. Polat, R. Demir, S. Kazan, and C. Yıldırım, “On Optimal Casorati Inequalities for $PTR$-Submanifolds of Complex Space Forms”, JNT, no. 55, pp. 47–57, June 2026, doi: 10.53570/jnt.1914322.
ISNAD
Polat, Gülistan - Demir, Ramazan - Kazan, Sema - Yıldırım, Cumali. “On Optimal Casorati Inequalities for $PTR$-Submanifolds of Complex Space Forms”. Journal of New Theory. 55 (June 1, 2026): 47-57. https://doi.org/10.53570/jnt.1914322.
JAMA
1.Polat G, Demir R, Kazan S, Yıldırım C. On Optimal Casorati Inequalities for $PTR$-Submanifolds of Complex Space Forms. JNT. 2026;:47–57.
MLA
Polat, Gülistan, et al. “On Optimal Casorati Inequalities for $PTR$-Submanifolds of Complex Space Forms”. Journal of New Theory, no. 55, June 2026, pp. 47-57, doi:10.53570/jnt.1914322.
Vancouver
1.Gülistan Polat, Ramazan Demir, Sema Kazan, Cumali Yıldırım. On Optimal Casorati Inequalities for $PTR$-Submanifolds of Complex Space Forms. JNT. 2026 Jun. 1;(55):47-5. doi:10.53570/jnt.1914322

 

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