9 citations · 22 across the 14 of their papers we have counts for
16 papers
Contact structures of type associated to solutions of Noth's equation
Matthew Randall
We establish a correspondence between solutions of Noth's equation, a non-linear ordinary differential equation that shows up in the theory of -distributions, and diffeomo…
Local equivalence of some maximally symmetric -distributions III: An-Nurowski surface rolling on a plane
Matthew Randall
We consider the maximally symmetric -distribution given by the An-Nurowski circle twistor bundle over the product of an An-Nurowski surface and the plane. This circle twis…
Local equivalence of some maximally symmetric -distributions II
Matthew Randall
We show the change of coordinates that maps the maximally symmetric -distribution given by solutions to the and generalised Chazy equation…
Local equivalence of some maximally symmetric -distributions
Matthew Randall
Using a complex parametrisation of , we show a change of coordinates that maps the maximally symmetric rolling -distribution to the flat Cartan distribution. This e…
A Monge normal form for the rolling distribution
Matthew Randall
Using a parametrisation of given by the second prolongation of the group action of unimodular fractional linear transformations as presented in an article of Clarkson and Ol…
Nurowski's conformal class of a maximally symmetric (2,3,5)-distribution and its Ricci-flat representatives
Matthew Randall
We show that the solutions to the second-order differential equation associated to the generalised Chazy equation with parameters and naturally show up in the conformal…
Automorphisms and transformations of solutions to the generalised Chazy equation for various parameters
Matthew Randall
We analyse the automorphisms of solutions to Chazy's equation and the generalised Chazy equation for the parameters and . These automorphisms are induced by triangular…
Automorphism of solutions to Ramanujan's differential equations and other results
Matthew Randall
In part one we prove a theorem about the automorphism of solutions to Ramanujan's differential equations. We also investigate possible applications of the result. In part two we pr…
Local equivalence of some maximally symmetric rolling distributions and Pfaffian systems
Matthew Randall
We give a description of Nurowski's conformal structure for some examples of bracket-generating rank 2 distributions in dimension 5, aka -distributions, namely the An-Nuro…
Three dimensional near-horizon metrics that are Einstein-Weyl
Matthew Randall
We investigate which three dimensional near-horizon metrics admit a compatible 1-form such that defines an Einstein-Weyl structure. We find explicit ex…
Schwarz triangle functions and duality for certain parameters of the generalised Chazy equation
Matthew Randall
Schwarz triangle functions play a fundamental role in the solutions of the generalised Chazy equation. Chazy has shown that for the parameters and , the equations can be l…
Flat -Distributions and Chazy's Equations
Matthew Randall
In the geometry of generic 2-plane fields on 5-manifolds, the local equivalence problem was solved by Cartan who also constructed the fundamental curvature invariant. For generic 2…
Generalised Ricci Solitons
Pawel Nurowski, Matthew Randall
We introduce a class of overdetermined systems of partial differential equations of finite type on (pseudo)-Riemannian manifolds that we call the generalised Ricci soliton equation…
The conformal-to-Einstein equation on Möbius surfaces
Matthew Randall
On a conformal manifold, it is well known that parallel sections of the standard tractor bundle with non-vanishing scale are in 1-1 correspondence with solutions of the conformal E…
Local obstructions to projective surfaces admitting skew-symmetric Ricci tensor
Matthew Randall
The equation determining whether a projective structure admits a connection in its given projective class that has skew-symmetric Ricci tensor is an overdetermined system of semi-l…
Local obstructions to a conformally invariant equation on Möbius surfaces
Matthew Randall
On a Möbius surface, as defined by D. Calderbank, we study a variant of the Einstein-Weyl (EW) equation which we call scalar-flat Möbius EW (sf-MEW). This is a conformally invarian…