η-Ricci solitons on 3-dimensional Kenmotsu manifolds

Shyam Kishor, Abhishek Singh
2020 SERIES III - MATEMATICS, INFORMATICS, PHYSICS  
The purpose of this paper is to study η-Ricci solitons on 3-dimensional Kenmotsu manifolds. First, we prove that an η-Ricci soliton on a 3-dimensional Kenmotsu manifold is an η-Einstein manifold. Besides these, we consider η-Ricci solitons on 3 -dimensional Kenmotsu manifolds with Ricci tensor of Codazzi type and cyclic parallel Ricci tensor. Next, we study conformally flat and ϕ-Ricci symmetric η-Ricci soliton on 3-dimensional Kenmotsu manifolds. Finally, we construct an example to prove the
more » ... mple to prove the existence of η-Ricci soliton on 3-dimensional Kenmotsu manifold and verify some results. 2000 Mathematics Subject Classification: 53C15, 53C25, 53D10. Key words: Ricci soliton, η-Ricci soliton, 3-dimensional Kenmotsu manifolds, Ricci tensor of Codazzi type, cyclic parallel Ricci tensor, ϕ-Ricci symmetric.
doi:10.31926/but.mif.2020.13.62.1.16 fatcat:5pzfutnntvc43koev7ah3c3kai