Einstein-Weyl structures from Hyper-Kähler metrics with conformal Killing vectors

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dc.creatorDunajski, Maciej
dc.creatorTod, Paul
dc.date1999-07-23
dc.date.accessioned2026-07-07T05:30:00Z
dc.date.available2026-07-07T05:30:00Z
dc.descriptionWe consider four (real or complex) dimensional hyper-Kähler metrics with a conformal symmetry K. The three-dimensional space of orbits of K is shown to have an Einstein-Weyl structure which admits a shear-free geodesics congruence for which the twist is a constant multiple of the divergence. In this case the Einstein-Weyl equations reduce down to a single second order PDE for one function. The Lax representation, Lie point symmetries, hidden symmetries and the recursion operator associated with this PDE are found, and some group invariant solutions are considered.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/9907146
dc.identifierhttp://arxiv.org/abs/math/9907146
dc.identifierDiffer.Geom.Appl. 14 (2001) 39-55
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78863
dc.subjectDifferential Geometry
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectExactly Solvable and Integrable Systems
dc.subject52B35, 53C55
dc.titleEinstein-Weyl structures from Hyper-Kähler metrics with conformal Killing vectors
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