η-Ricci–Yamabe Solitons along Riemannian Submersions

Siddiqi M. D., Mofarreh F., Akyol M. A., Hakami A. H.

Axioms, vol.12, no.8, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 8
  • Publication Date: 2023
  • Doi Number: 10.3390/axioms12080796
  • Journal Name: Axioms
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: homotopy groups, Riemannian manifold, Riemannian submersion, η-Ricci–Yamabe soliton
  • Uşak University Affiliated: No

Abstract

In this paper, we investigate the geometrical axioms of Riemannian submersions in the context of the (Formula presented.) -Ricci–Yamabe soliton ((Formula presented.) -RY soliton) with a potential field. We give the categorization of each fiber of Riemannian submersion as an (Formula presented.) -RY soliton, an (Formula presented.) -Ricci soliton, and an (Formula presented.) -Yamabe soliton. Additionally, we consider the many circumstances under which a target manifold of Riemannian submersion is an (Formula presented.) -RY soliton, an (Formula presented.) -Ricci soliton, an (Formula presented.) -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 (Formula presented.) of the soliton is of gradient type =:grad (Formula presented.) and provide some examples of an (Formula presented.) -RY soliton, which illustrates our finding. Finally, we explore a number theoretic approach to Riemannian submersion with totally geodesic fibers.