η-Ricci–Yamabe Solitons along Riemannian Submersions

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

Axioms, cilt.12, sa.8, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 8
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3390/axioms12080796
  • Dergi Adı: Axioms
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: homotopy groups, Riemannian manifold, Riemannian submersion, η-Ricci–Yamabe soliton
  • Uşak Üniversitesi Adresli: Hayır

Özet

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.