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Classification of Warped Product Submanifolds in Kenmotsu Space Forms Admitting Gradient Ricci Solitons

Author

Listed:
  • Ali H. Alkhaldi

    (Department of Mathematics, College of Science, King Khalid University, 9004 Abha, Saudi Arabia)

  • Akram Ali

    (Department of Mathematics, College of Science, King Khalid University, 9004 Abha, Saudi Arabia)

Abstract

The purpose of this article is to obtain geometric conditions in terms of gradient Ricci curvature, both necessary and sufficient, for a warped product semi-slant in a Kenmotsu space form, to be either CR-warped product or simply a Riemannian product manifold when a basic inequality become equality. The next purpose of this paper to find the necessary condition admitting gradient Ricci soliton, that the warped product semi-slant submanifold of Kenmotsu space form, is an Einstein warped product. We also discuss some obstructions to these constructions in more detail.

Suggested Citation

  • Ali H. Alkhaldi & Akram Ali, 2019. "Classification of Warped Product Submanifolds in Kenmotsu Space Forms Admitting Gradient Ricci Solitons," Mathematics, MDPI, vol. 7(2), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:112-:d:199792
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    References listed on IDEAS

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    1. Jong Ryul Kim, 2018. "Remarks on the Warped Product Structure from the Hessian of a Function," Mathematics, MDPI, vol. 6(12), pages 1-8, November.
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    Cited by:

    1. Akram Ali & Fatemah Mofarreh, 2020. "Geometric Inequalities of Bi-Warped Product Submanifolds of Nearly Kenmotsu Manifolds and Their Applications," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    2. Nadia Alluhaibi & Fatemah Mofarreh & Akram Ali & Wan Ainun Mior Othman, 2020. "Geometric Inequalities of Warped Product Submanifolds and Their Applications," Mathematics, MDPI, vol. 8(5), pages 1-11, May.

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