Non-singular solutions to the normalized Ricci flow equation

2006/09/09 by Fuquan Fang, Fang, Fuquan, Yuguang Zhang +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0609254

openalex publication_date 2006/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study non-singular solutions of Ricci flow on a closed manifold of dimension at least 4. Amongst others we prove that, if M is a closed 4-manifold on which the normalized Ricci flow exists for all time t>0 with uniformly bounded sectional curvature, then the Euler characteristic χ(M)≥ 0. Moreover, the 4-manifold satisfies one of the following \noindent (i) M is a shrinking Ricci solition; \noindent (ii) M admits a positive rank F-structure; \noindent (iii) the Hitchin-Thorpe type inequality holds 2χ(M)≥ 3|τ(M)| where χ(M) (resp. τ(M)) is the Euler characteristic (resp. signature) of M.

Citations

• A Compactness Property for Solutions of the Ricci Flow

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