Integral pinched gradient shrinking ρ-Einstein solitons

2016/12/27 by Guangyue Huang, Huang, Guangyue
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1612.08512

openalex publication_date 2016/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The gradient shrinking \ρ-Einstein soliton is a triple (Mⁿ,g,f) such\nthat R_ij+f_ij=(
rho R+
lambda) g_ij, where (Mⁿ,g) is a Riemannian\nmanifold, \λ>0, \ρ\∈\ℝ\∖ 0 and f is the potential\nfunction on Mⁿ. In this paper, using algebraic curvature estimates and the\nYamabe-Sobolev inequality, we prove some integral pinching rigidity results for\ncompact gradient shrinking \ρ-Einstein solitons.\n

Citations

• Fourth order curvature flows and geometric applications
• Rigidity of gradient Einstein shrinkers

Related

• Rigidity of gradient Einstein shrinkers
• Ends of shrinking gradient ρ-Einstein solitons
• Rigidity results for Riemann solitons
• Compact gradient ρ-Einstein soliton is isometric to the Euclidean sphere
• The Curvature of Gradient Ricci Solitons