A rigidity theorem for codimension one shrinking gradient Ricci solitons in \mathbb Rⁿ⁺¹

2014/10/21 by Pengfei Guan, Peng Lü, Guan, Pengfei +3
Mathematics · Physics and Astronomy · #53C #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1410.5856

openalex publication_date 2014/10/21 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We prove a splitting theorem for complete gradient Ricci soliton with nonnegative curvature and establish a rigidity theorem for codimension one complete shrinking gradient Ricci soliton in \mathbb Rⁿ⁺¹ with nonnegative Ricci curvature.

Citations

• Ricci flow with surgery on three-manifolds
• On shrinking Gradient Ricci Soliton With Nonnegative Sectional Curvature

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