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Vanishing Homology of Warped Product Submanifolds in Complex Space Forms and Applications

Author

Listed:
  • Ali H. Alkhaldi

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, 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)

  • Izhar Ahmad

    (Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
    Center for Intelligent Secure Systems, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Akram Ali

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

Abstract

In this paper, we prove the nonexistence of stable integral currents in compact oriented warped product pointwise semi-slant submanifold M n of a complex space form M ˜ ( 4 ϵ ) under extrinsic conditions which involve the Laplacian, the squared norm gradient of the warped function, and pointwise slant functions. We show that i -the homology groups of M n are vanished. As applications of homology groups, we derive new topological sphere theorems for warped product pointwise semi-slant submanifold M n , in which M n is homeomorphic to a sphere S n if n ≥ 4 and if n = 3 , then M 3 is homotopic to a sphere S 3 under the assumption of extrinsic conditions. Moreover, the same results are generalized for CR-warped product submanifolds.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3884-:d:947475
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    References listed on IDEAS

    as
    1. Fatemah Mofarreh & Akram Ali & Nadia Alluhaibi & Olga Belova & Hang Xu, 2021. "Ricci Curvature for Warped Product Submanifolds of Sasakian Space Forms and Its Applications to Differential Equations," Journal of Mathematics, Hindawi, vol. 2021, pages 1-15, January.
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    Cited by:

    1. 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.

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