Gradient Shrinking Sasaki-Ricci Solitons with Harmonic Weyl Tensor

2025/09/01 by Shu-Cheng Chang, Chang, Shu-Cheng, Hongbing Qiu +1
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.2509.01100

openalex publication_date 2025/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish integral curvature estimates for complete gradient shrinking Sasaki-Ricci solitons. As an application, we show that any such soliton with harmonic Weyl tensor must be a finite quotient of a sphere. This result can be regarded as the Sasaki analogue of the work of Munteanu and Sesum [15] on Ricci solitons.

Citations

• Transverse Rigidity of Shrinking Sasaki-Ricci Solitons
• On the existence of conic Sasaki-Einstein metrics on log Fano Sasakian manifolds of dimension five
• On the convergence of the Sasaki-Ricci flow
• On gradient Ricci solitons
• Gradient Shrinking Solitons with Vanishing Weyl Tensor
• On Locally Conformally Flat Gradient Shrinking Ricci Solitons
• On a classification of the gradient shrinking solitons
• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds
• Manifolds with positive curvature operators are space forms

Related

• On gradient Ricci solitons
• Gradient shrinking Ricci solitons of half harmonic Weyl curvature
• Geometry and Topology of Gradient Shrinking Sasaki-Ricci Solitons
• The Curvature of Gradient Ricci Solitons
• Gradient Shrinking Ricci Solitons and Modified Sectional Curvature