On the structure of almost Yamabe solitons

2025/11/03 by Seungsu Hwang, Hwang, Seungsu, Gabjin Yun +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations #Primary 53C21 #Secondary 53C24

paper · pdf · doi:10.48550/arxiv.2511.01429

openalex publication_date 2025/11/03 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

Abstract

In this paper, we study structures of almost Yamabe solitons which are not necessarily gradient. First, we investigate conditions that both compact and noncompact almost Yamabe solitons become trivial solitons which means the given vector field is a Killing vector field. Second, we show that an almost Yamabe soliton whose vector field is closed admits a local warped product structure with a one-dimensional base. This result can be considered as a generalization of a result in \citec-s-z and \citec-m-m

Citations

• Classification of almost Yamabe solitons in Euclidean spaces
• A note on compact gradient Yamabe solitons
• The classification of locally conformally flat Yamabe solitons
• Rigidity of gradient Ricci Solitons
• Twisted products in pseudo-Riemannian geometry

Related

• Classification of almost Yamabe solitons in Euclidean spaces
• A note on warped product almost quasi-Yamabe solitons
• Immersion of gradient almost Yamabe solitons into warped product manifolds
• Rigidity results for quotient almost Yamabe solitons
• On Warped Product Gradient Yamabe Solitons