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Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures
(ElsevierDifferential Geometry and its Application, 2016-11-11)
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 ...
Non-relativistic twistor theory and Newton-Cartan geometry
(SpringerCommunications in Mathematical Physics, 2016-01-14)
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 ...
On the quadratic invariant of binary sextics
(Cambridge University PressMathematical Proceedings of the Cambridge Philosophical Society, 2016-07-28)
We provide a geometric characterisation of binary sextics with vanishing quadratic invariant.
Metrisability of three-dimensional path geometries
(SpringerEuropean Journal of Mathematics, 2016-03-08)
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 ...
First integrals of affine connections and Hamiltonian systems of hydrodynamic type
(Oxford University PressJournal of Integrable Systems, 2016-12-23)
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 ...