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Gradient Expanding Ricci Solitons Type Inequalities on Submanifolds in Quaternion Kaehler Manifolds with Bi-Slant Factor

Author

Listed:
  • Ali H. Hakami

    (Department of Mathematics, College of Science, Jazan University, P.O. Box 277, Jazan 4512, Saudi Arabia)

  • Mohd Danish Siddiqi

    (Department of Mathematics, College of Science, Jazan University, P.O. Box 277, Jazan 4512, Saudi Arabia)

Abstract

In this article, we study the Ricci soliton on quaternion bi-slant submanifolds of quaternion Kaehler manifolds. We obtain a lower-bound-type inequality in terms of expanding gradient Ricci solitons with a gradient-type vector field for the quaternion bi-slant submanifold of quaternion Kaehler manifolds. Additionally, we derive a series of lower-bound-type inequalities for semi-slant submanifolds, C R -submanifolds, hemi-slant submanifolds, slant submanifolds, invariant anti-invaraint submanifolds and totally real submanifolds in the same quaternion Kaehler manifolds. Finally, we discuss a double inequality for expanding gradient Ricci solitons on submanifolds in quaternion Kaehler manifolds and extend the same double inequality in terms of gradient Ricci solitons with a scalar concircular field on semi-slant, quaternion C R -submanifolds of quaternion Kaehler manifolds.

Suggested Citation

  • Ali H. Hakami & Mohd Danish Siddiqi, 2026. "Gradient Expanding Ricci Solitons Type Inequalities on Submanifolds in Quaternion Kaehler Manifolds with Bi-Slant Factor," Mathematics, MDPI, vol. 14(2), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:2:p:357-:d:1845612
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