Browsing Department of Materials Science and Metallurgy by Author "Dunajski, Maciej Lukasz"
Now showing items 1-9 of 9
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Einstein–Weyl spaces and near-horizon geometry
Dunajski, Maciej Lukasz; Gutowski, J; Sabra, W (IOP PublishingClassical and Quantum Gravity, 2017-02-02)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 ...
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First integrals of affine connections and Hamiltonian systems of hydrodynamic type
Contatto, F; Dunajski, Maciej Lukasz (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 ...
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Manton's five vortex equations from self-duality
Contatto, F; Dunajski, Maciej Lukasz (Journal of Physics A: Mathematical and Theoretical, 2017-08-17)
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Metrisability of three-dimensional path geometries
Dunajski, Maciej Lukasz; Eastwood, Michael (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 ...
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Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures
Dunajski, Maciej Lukasz; Tod, P (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 ...
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Non-relativistic twistor theory and Newton-Cartan geometry
Dunajski, Maciej Lukasz; Gundry, James (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 ...
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On the Einstein-Weyl and conformal self-duality equations
Dunajski, Maciej Lukasz; Ferapontov, EV; Kruglikov, B (AIP PublishingJournal of Mathematical Physics, 2015-08-03)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 ...
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On the quadratic invariant of binary sextics
Dunajski, Maciej Lukasz; Penrose, Roger (Cambridge University PressMathematical Proceedings of the Cambridge Philosophical Society, 2016-07-28)We provide a geometric characterisation of binary sextics with vanishing quadratic invariant.
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Twistor theory at fifty: from contour integrals to twistor strings.
Atiyah, Michael; Dunajski, Maciej Lukasz; Mason, Lionel J (Proceedings. Mathematical, physical, and engineering sciences, 2017-10-11)