Nurowski's conformal class of a maximally symmetric (2,3,5)-distribution and its Ricci-flat representatives

2019/03/06 by Matthew Randall, Randall, Matthew
Mathematics · #34A05 #34A34 (primary) #53A30 #58A15 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.DG #msc:34A05 #msc:34A34 #msc:53A30 #msc:58A15

paper · pdf · doi:10.48550/arxiv.1903.02245

15 pages

arxiv created 2019/03/06 · openalex publication_date 2019/03/06 · arxiv updated 2019/03/07 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We show that the solutions to the second-order differential equation associated to the generalised Chazy equation with parameters k=2 and k=3 naturally show up in the conformal rescaling that takes a representative metric in Nurowski's conformal class associated to a maximally symmetric (2,3,5)-distribution (described locally by a certain function φ(x,q)=(q²)/(H''(x))) to a Ricci-flat one.

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