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Geometry of Bi-Warped Product Submanifolds of Nearly Trans-Sasakian Manifolds

Author

Listed:
  • Ali H. Alkhaldi

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

  • Akram Ali

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

Abstract

In the present work, we consider two types of bi-warped product submanifolds, M = M T × f 1 M ⊥ × f 2 M ϕ and M = M ϕ × f 1 M T × f 2 M ⊥ , in nearly trans-Sasakian manifolds and construct inequalities for the squared norm of the second fundamental form. The main results here are a generalization of several previous results. We also design some applications, in view of mathematical physics, and obtain relations between the second fundamental form and the Dirichlet energy. The relationship between the eigenvalues and the second fundamental form is also established.

Suggested Citation

  • Ali H. Alkhaldi & Akram Ali, 2021. "Geometry of Bi-Warped Product Submanifolds of Nearly Trans-Sasakian Manifolds," Mathematics, MDPI, vol. 9(8), pages 1-24, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:847-:d:535096
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