We show that a class of solutions of minimal supergravity in five dimensions is given by lifts of three-dimensional Einstein–Weyl structures of hyper-CR type. We characterise this class as most general near-horizon limits ...

We find necessary and sufficient conditions for a local geodesic flow of an affine connection on a surface to admit a linear first integral. The conditions are expressed in terms of two scalar invariants of differential ...

Given a projective structure on a three-dimensional manifold, we find explicit obstructions to the local existence of a Levi-Civita connection in the projective class. These obstructions are given by projectively invariant ...

Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in a basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly ...

We develop a non-relativistic twistor theory, in which Newton-Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle O ⊕ O(2). We ...

The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be regarded as ‘master dispersionless systems’ in four and three dimensions respectively. Their integrability by twistor methods has been ...

We provide a geometric characterisation of binary sextics with vanishing quadratic invariant.