|DATE||January 24 (Wed), 2018|
|TITLE||Flat (2,3,5)-distributions and Chazy's equations|
In the theory of generic 2-plane fields on 5-manifolds, or (2,3,5)-distributions, the local equivalence problem was solved by Élie Cartan who also constructed the fundamental curvature invariant. For these distributions described by a single function of the form F(q), the vanishing condition for the curvature invariant is given by a 6th order nonlinear ODE. Furthermore, Daniel An and Pawel Nurowski have shown that this ODE is the Legendre transform of the nonlinear ODE that appeared in Gottfried Noth's thesis in 1904.