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Three dimensional near-horizon metrics that are Einstein-Weyl

Matthew Randall — 2017

Archivum Mathematicum

We investigate which three dimensional near-horizon metrics $g_{N H}$ admit a compatible 1-form $X$ such that $(X, [g_{N H}])$ defines an Einstein-Weyl structure. We find explicit examples and see that some of the solutions give rise to Einstein-Weyl structures of dispersionless KP type and dispersionless Hirota (aka hyperCR) type.

Local equivalence of some maximally symmetric $(2, 3, 5)$ -distributions II

Matthew Randall — 2025

Archivum Mathematicum

We show the change of coordinates that maps the maximally symmetric $(2, 3, 5)$ -distribution given by solutions to the $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy equation to the flat Cartan distribution. This establishes the local equivalence between the maximally symmetric $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy distribution and the flat Cartan or Hilbert-Cartan distribution. We give the set of vector fields parametrised by solutions to the $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy equation and the corresponding Ricci-flat conformal scale that bracket-generate...

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Three dimensional near-horizon metrics that are Einstein-Weyl

Local equivalence of some maximally symmetric $(2, 3, 5)$ -distributions II

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Currently displaying 1 – 2 of 2

Three dimensional near-horizon metrics that are Einstein-Weyl

Local equivalence of some maximally symmetric ( 2 , 3 , 5 ) -distributions II

Local equivalence of some maximally symmetric $(2, 3, 5)$ -distributions II