η-Ricci–Yamabe Solitons along Riemannian Submersions
Mohd Danish Siddiqi, Fatemah Mofarreh, Mehmet Akif Akyol, Ali H. Hakami
Abstract
In this paper, we investigate the geometrical axioms of Riemannian submersions in the context of the η-Ricci–Yamabe soliton (η-RY soliton) with a potential field. We give the categorization of each fiber of Riemannian submersion as an η-RY soliton, an η-Ricci soliton, and an η-Yamabe soliton. Additionally, we consider the many circumstances under which a target manifold of Riemannian submersion is an η-RY soliton, an η-Ricci soliton, an η-Yamabe soliton, or a quasi-Yamabe soliton. We deduce a Poisson equation on a Riemannian submersion in a specific scenario if the potential vector field ω of the soliton is of gradient type =:grad(γ) and provide some examples of an η-RY soliton, which illustrates our finding. Finally, we explore a number theoretic approach to Riemannian submersion with totally geodesic fibers.