An optimal inequality for warped product submanifolds in complex space forms

Md Aquib; Md Aquib

doi:10.3934/math.2025804

AIMS Mathematics

2025, Volume 10, Issue 8: 18055-18069. doi: 10.3934/math.2025804

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Research article

An optimal inequality for warped product submanifolds in complex space forms

Md Aquib ^,

Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box-65892, Riyadh 11566, Saudi Arabia

Received: 27 December 2024 Revised: 23 June 2025 Accepted: 23 July 2025 Published: 08 August 2025
MSC : 53B25, 53C40, 53C25, 53C21

In this work, using optimization procedures on Riemannian submanifolds, we obtained two different inequalities on the generalized normalized $ \delta $-Casorati curvatures of warped product submanifolds in complex space forms. We also quantified the conditions under which these inequalities become equalities, providing more insight into their geometric consequences. Further, we described new findings in the form of harmonic functions and Hessian functions, which offer a more general view of the interplay between curvature and analyticity.
- Casorati curvature,
- warped product submanifold,
- complex space form,
- harmonic function,
- Hessian function
Citation: Md Aquib. An optimal inequality for warped product submanifolds in complex space forms[J]. AIMS Mathematics, 2025, 10(8): 18055-18069. doi: 10.3934/math.2025804

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Abstract

In this work, using optimization procedures on Riemannian submanifolds, we obtained two different inequalities on the generalized normalized $ \delta $-Casorati curvatures of warped product submanifolds in complex space forms. We also quantified the conditions under which these inequalities become equalities, providing more insight into their geometric consequences. Further, we described new findings in the form of harmonic functions and Hessian functions, which offer a more general view of the interplay between curvature and analyticity.

References

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