Evolutions of S³ and ℝP³ that describe Eguchi-Hanson metric and metrics of constant curvature

2014/11/16 by Evgeny G. Malkovich, Malkovich, Evgeny G.
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1411.4234

arxiv created 2014/11/16 · openalex publication_date 2014/11/16 · arxiv updated 2014/11/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this work we illustrate some well-known facts about the evolution of S³ under the Ricci flow. The Dirac flow we introduce allows us to describe the 4- dimensional metrics with constant curvature. Another new flow leads to the Eguchi-Hanson metric and can be defined either on metric or on corresponding contact forms.

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