Generalized Ricci flow II: existence for noncompact complete manifolds

2013/09/30 by Yi Li, Li, Yi
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1309.7710

64 pages

arxiv created 2013/09/30 · openalex publication_date 2013/09/30 · arxiv updated 2013/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we continue to study the generalized Ricci flow. We give a criterion on steady gradient Ricci soliton on complete and noncompact Riemannian manifolds that is Ricci-flat, and then introduce a natural flow whose stable points are Ricci-flat metrics. Modifying the argument used by Shi and List, we prove the short time existence and higher order derivatives estimates.

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