Four-dimensional generalized Ricci flows with nilpotent symmetry

2021/09/15 by Steven Gindi, Jeffrey Streets, Gindi, Steven +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2109.07562

openalex publication_date 2021/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study solutions to generalized Ricci flow on four-manifolds with a nilpotent, codimension 1 symmetry. We show that all such flows are immortal, and satisfy type III curvature and diameter estimates. Using a new kind of monotone energy adapted to this setting, we show that blowdown limits lie in a canonical finite-dimensional family of solutions. The results are new for Ricci flow.

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