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Mathematics
Volume 13
Issue 10
10.3390/math13101643
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Article

Optimal Inequalities Characterizing Totally Real Submanifolds in Quaternionic Space Form

by
Fatimah Alghamdi
1,*,† and
Akram Ali
2,†
1
Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia
2
Department of Mathematics, College of Science, King Khalid University, Abha 9004, Saudi Arabia
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2025, 13(10), 1643; https://doi.org/10.3390/math13101643 (registering DOI)
Submission received: 11 March 2025 / Revised: 26 April 2025 / Accepted: 12 May 2025 / Published: 17 May 2025
(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)
Versions Notes

Abstract

In the present paper, we investigate some pinching inequalities on the scalar curvature of a totally real submanifold in quaternionic space form that leads to a topological conclusion of the submanifold. In addition, we construct another inequality which includes the mean curvature and the length of the second fundamental form.
Keywords: totally real submanifold; second fundamental form; rigidity theorems; scalar curvature; space form; mean curvature totally real submanifold; second fundamental form; rigidity theorems; scalar curvature; space form; mean curvature

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MDPI and ACS Style

Alghamdi, F.; Ali, A. Optimal Inequalities Characterizing Totally Real Submanifolds in Quaternionic Space Form. Mathematics 2025, 13, 1643. https://doi.org/10.3390/math13101643

AMA Style

Alghamdi F, Ali A. Optimal Inequalities Characterizing Totally Real Submanifolds in Quaternionic Space Form. Mathematics. 2025; 13(10):1643. https://doi.org/10.3390/math13101643

Chicago/Turabian Style

Alghamdi, Fatimah, and Akram Ali. 2025. "Optimal Inequalities Characterizing Totally Real Submanifolds in Quaternionic Space Form" Mathematics 13, no. 10: 1643. https://doi.org/10.3390/math13101643

APA Style

Alghamdi, F., & Ali, A. (2025). Optimal Inequalities Characterizing Totally Real Submanifolds in Quaternionic Space Form. Mathematics, 13(10), 1643. https://doi.org/10.3390/math13101643

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