Complete Yamabe solitons with finite total scalar curvature

2017/11/21 by Shun Maeta, Maeta, Shun
Mathematics · Physics and Astronomy · #53C20 #53C21 #53C25 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1711.07623

openalex publication_date 2017/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that steady or shrinking complete gradient Yamabe solitons with finite total scalar curvature and non-positive Ricci curvature are Ricci flat. Moreover, under certain pinching condition for Ricci curvature, we show that steady or shrinking complete gradient Yamabe solitons with finite total scalar curvature and non-positive scalar curvature have zero scalar curvature.

Related

• Remarks on scalar curvature of Yamabe solitons
• Complete quasi-Yamabe gradient solitons with bounded scalar curvature
• On a class of complete non-compact gradient Yamabe solitons
• 3-dimensional complete gradient Yamabe solitons with divergence-free Cotton tensor
• Classification of low-dimensional complete gradient Yamabe solitons