Rigidity of five-dimensional quasi-Einstein manifolds with constant scalar curvature

2025/11/20 by Zhong Cao, Cao, Zhongxian
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.2511.16128

openalex publication_date 2025/11/20 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28

Abstract

Let (M⁵,g) be a five-dimensional non-trivial simply-connected compact quasi-Einstein manifold with boundary. If M has constant scalar R, Johnatan Costa, Ernani Ribeiro Jr, and Detang Zhou show that R = ((m-5)k+20)/(m-k+4)λ for some k∈\0,2,3,4\. Both cases of k=0 and k=4 are already classified. In this paper we will prove that the case k=3 is rigid.

Citations

• On quasi-Einstein manifolds with constant scalar curvature
• Four-dimensional shrinkers with nonnegative Ricci curvature
• Rigidity of Five-dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature
• Rigidity of compact quasi-Einstein manifolds with boundary
• Rigidity of quasi-Einstein metrics: The incompressible case
• Remarks on compact quasi-Einstein manifolds with boundary
• Compact quasi-Einstein manifolds with boundary
• Noncompact quasi-Einstein manifolds conformal to a Euclidean space
• Warped product Einstein metrics over spaces with constant scalar curvature
• Smooth metric measure spaces and quasi-Einstein metrics
• On the classification of warped product Einstein metrics
• Geometry of isoparametric hypersurfaces in Riemannian manifolds
• Isoparametric functions and exotic spheres
• Rigidity of Quasi-Einstein Metrics
• Comparison Geometry for the Bakry-Emery Ricci Tensor
• Conformally flat manifolds with nonnegative Ricci curvature

Related

• Rigidity of compact quasi-Einstein manifolds with boundary
• Compact gradient Einstein-type manifolds with boundary and constant scalar curvature
• On generalized quasi-Einstein manifolds
• Compact quasi-Einstein manifolds with boundary
• On quasi-Einstein manifolds with constant scalar curvature