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The Homology of Warped Product Submanifolds of Spheres and Their Applications

Author

Listed:
  • Lamia Saeed Alqahtani

    (Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Akram Ali

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

  • Pişcoran Laurian-Ioan

    (Department of Mathematics and Computer Science Victoriei 76, North Center of Baia Mare Technical University of Cluj Napoca, 430122 Baia Mare, Romania)

  • Ali H. Alkhaldi

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

Abstract

The aim of the current article is to formulate sufficient conditions for the Laplacian and a gradient of the warping function of a compact warped product submanifold Σ β 1 + β 2 in a unit sphere S d that provides trivial homology and fundamental groups. We also validate the instability of current flows in π 1 ( Σ β 1 + β 2 ) . The constraints are also applied to the warped function eigenvalues and integral Ricci curvatures.

Suggested Citation

  • Lamia Saeed Alqahtani & Akram Ali & Pişcoran Laurian-Ioan & Ali H. Alkhaldi, 2023. "The Homology of Warped Product Submanifolds of Spheres and Their Applications," Mathematics, MDPI, vol. 11(15), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3405-:d:1210511
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    References listed on IDEAS

    as
    1. Ali H. Alkhaldi & Pişcoran Laurian-Ioan & Izhar Ahmad & Akram Ali, 2022. "Vanishing Homology of Warped Product Submanifolds in Complex Space Forms and Applications," Mathematics, MDPI, vol. 10(20), pages 1-17, October.
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