2020/03/20 by Shahroud Azami, Azami, Shahroud
Mathematics · Physics and Astronomy · #53C15 #53C25 #53C44 #Advanced Differential Geometry Research #FOS: Mathematics #General Mathematics (math.GM) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2004.01776
openalex publication_date 2020/03/20 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
The object of the present paper is to study β-almost Yamabe solitons and β-almost Ricci solitons on almost co-Kähler manifolds. In this paper, we prove that if an almost co-Kähler manifold M with the Reeb vector field ξ admits a β-almost Yamabe solitons with the potential vector field ξ or bξ, where b is a smooth function then manifold is K-almost co-Kähler manifold or the soliton is trivial, respectively. Also, we show if a closed (κ,μ)-almost co-Kähler manifold with n>1 and κ<0 admits a β-almost Yamabe soliton then the soliton is trivial and expanding. Then we study an almost co-Kähler manifold admits a β-almost Yamabe soliton or β-almost Ricci soliton with V as the potential vector field, V is a special geometric vector field.