81 citations · 175 across the 30 of their papers we have counts for
5 papers · 1 filter
Asymptotically shearfree congruences in (2,2) spacetimes and Burgers' equation
Jonathan Holland, George Sparling
The paper proves that any asymptotically shearfree congruence at the conformal infinity (scri) in a (2,2)-signature spacetime is determined locally by a solution to the pair of for…
Causal geometries, null geodesics, and gravity
Jonathan Holland, George Sparling
The authors study a generalized notion of null geodesic defined by the Legendrian dynamics of a regular conical subbundle of the tangent bundle on a manifold. A natural extension o…
Causal geometries and third-order ordinary differential equations
Jonathan Holland, George Sparling
We discuss contact invariant structures on the space of solutions of a third-order ordinary differential equation. Associated to any third-order differential equation modulo contac…
3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations
Pawel Nurowski, George A J Sparling
The equivalence problem for second order ODEs given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate 3-dimensional CR structures…
Conformally invariant powers of the ambient Dirac operator
Jonathan Holland, George Sparling
This paper constructs a family of conformally invariant differential operators acting on spinor densities with leading part a power of the Dirac operator. The construction applies…