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

Scalar curvature, mean curvature, Casorati curvature, complex space form, partially totally real submanifold

References

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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