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

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)-KM), 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.