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Geometric Inequalities of Warped Product Submanifolds and Their Applications

Author

Listed:
  • Nadia Alluhaibi

    (Department of Mathematics, Science and Arts College, Rabigh Campus, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Fatemah Mofarreh

    (Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia)

  • Akram Ali

    (Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia)

  • Wan Ainun Mior Othman

    (Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia)

Abstract

In the present paper, we prove that if Laplacian for the warping function of complete warped product submanifold M m = B p × h F q in a unit sphere S m + k satisfies some extrinsic inequalities depending on the dimensions of the base B p and fiber F q such that the base B p is minimal, then M m must be diffeomorphic to a unit sphere S m . Moreover, we give some geometrical classification in terms of Euler–Lagrange equation and Hamiltonian of the warped function. We also discuss some related results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:759-:d:356407
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    References listed on IDEAS

    as
    1. 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.
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