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Solitons Equipped with a Semi-Symmetric Metric Connection with Some Applications on Number Theory

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)

  • Aliya Naaz Siddiqui

    (Division of Mathematics, School of Basic Sciences, Galgotias University, Greater Noida 203201, India)

  • Kamran Ahmad

    (Division of Mathematics, School of Basic Sciences, Galgotias University, Greater Noida 203201, India)

Abstract

A solution to an evolution equation that evolves along symmetries of the equation is called a self-similar solution or soliton. In this manuscript, we present a study of η -Ricci solitons ( η -RS) for an interesting manifold called the ( ε ) -Kenmotsu manifold ( ( ε ) - K M ), endowed with a semi-symmetric metric connection (briefly, a SSM-connection). We discuss Ricci and η -Ricci solitons with a SSM-connection satisfying certain curvature restrictions. In addition, we consider the characteristics of the gradient η -Ricci solitons (a special case of η -Ricci soliton), with a Poisson equation on the same ambient manifold for a SSM-connection. In addition, we derive an inequality for the lower bound of gradient η -Ricci solitons for ( ε ) -Kenmotsu manifold, with a semi-symmetric metric connection. Finally, we explore a number theoretic approach in the form of Pontrygin numbers to the ( ε ) -Kenmotsu manifold equipped with a semi-symmetric metric connection.

Suggested Citation

  • Ali H. Hakami & Mohd. Danish Siddiqi & Aliya Naaz Siddiqui & Kamran Ahmad, 2023. "Solitons Equipped with a Semi-Symmetric Metric Connection with Some Applications on Number Theory," Mathematics, MDPI, vol. 11(21), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4452-:d:1268670
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    References listed on IDEAS

    as
    1. Mukut Mani Tripathi & Erol Kılıç & Selcen Yüksel Perktaş & Sadık Keleş, 2010. "Indefinite Almost Paracontact Metric Manifolds," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-19, April.
    2. A. Bejancu & K. L. Duggal, 1993. "Real hypersurfaces of indefinite Kaehler manifolds," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 16, pages 1-12, January.
    3. Vandana & Rajeev Budhiraja & Aliya Naaz Siddiqui & Ali Hussain Alkhaldi, 2023. "Solitonic View of Generic Contact CR-Submanifolds of Sasakian Manifolds with Concurrent Vector Fields," Mathematics, MDPI, vol. 11(12), pages 1-9, June.
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