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Warped Product Pointwise Semi Slant Submanifolds of Sasakian Space Forms and their Applications

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  • Nadia Alluhaibi
  • Meraj Ali Khan

Abstract

In this study, we attain some existence characterizations for warped product pointwise semi slant submanifolds in the setting of Sasakian space forms. Moreover, we investigate the estimation for the squared norm of the second fundamental form and further discuss the case of equality. By the application of attained estimation, we obtain some classifications of these warped product submanifolds in terms of Ricci soliton and Ricci curvature. Further, the formula for Dirichlet energy of involved warping function is derived. A nontrivial example of such warped product submanifolds is also constructed. Throughout the paper, we will use the following acronyms: “WP” for warped product, “WF” for warping function, “AC” for almost contact, and “WP‐PSS” for the warped product pointwise semi slant.

Suggested Citation

  • Nadia Alluhaibi & Meraj Ali Khan, 2020. "Warped Product Pointwise Semi Slant Submanifolds of Sasakian Space Forms and their Applications," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:5654876
    DOI: 10.1155/2020/5654876
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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.
    2. 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.
    3. Falleh R. Al-Solamy & Meraj Ali Khan, 2012. "Semi-Slant Warped Product Submanifolds of a Kenmotsu Manifold," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-10, June.
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