Optimal Inequalities Characterizing Totally Real Submanifolds in Quaternionic Space Form

Fatimah Alghamdi () and Akram Ali
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Fatimah Alghamdi: Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia
Akram Ali: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia

Mathematics, 2025, vol. 13, issue 10, 1-11

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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