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

Ali H. Hakami, Mohd. Danish Siddiqi (), Aliya Naaz Siddiqui and Kamran Ahmad
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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

Mathematics, 2023, vol. 11, issue 21, 1-14

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.

Keywords: ( ? )-Kenmotsu manifold; SSM-connection; ? -Ricci soliton; Pontrygin numbers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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