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Some Pinching Results for Bi-Slant Submanifolds in S -Space Forms

Author

Listed:
  • Mohd Aquib

    (Department of Mathematics, Sri Venkateswara College, University of Delhi, New Delhi-110021, India
    These authors contributed equally to this work.)

  • Meraj Ali Khan

    (Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
    These authors contributed equally to this work.)

  • Adela Mihai

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania
    Interdisciplinary Doctoral School, Transilvania University of Braşov, 500036 Braşov, Romania
    These authors contributed equally to this work.)

  • Ion Mihai

    (Department of Mathematics, University of Bucharest, 010014 Bucharest, Romania
    These authors contributed equally to this work.)

Abstract

The objective of the present article is to prove two geometric inequalities for submanifolds in S -space forms. First, we establish inequalities for the generalized normalized δ -Casorati curvatures for bi-slant submanifolds in S -space forms and then we derive the generalized Wintgen inequality for Legendrian and bi-slant submanifolds in the same ambient space. We also discuss the equality cases of the inequalities. Further, we provide some immediate geometric applications of the results. Finally, we construct some examples of slant and Legendrian submanifolds, respectively.

Suggested Citation

  • Mohd Aquib & Meraj Ali Khan & Adela Mihai & Ion Mihai, 2022. "Some Pinching Results for Bi-Slant Submanifolds in S -Space Forms," Mathematics, MDPI, vol. 10(9), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1538-:d:808047
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    References listed on IDEAS

    as
    1. Yanlin Li & Akram Ali & Rifaqat Ali, 2021. "A General Inequality for CR-Warped Products in Generalized Sasakian Space Form and Its Applications," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-6, August.
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