Mathematics – Differential Geometry
Scientific paper
1999-07-23
Differ.Geom.Appl. 14 (2001) 39-55
Mathematics
Differential Geometry
14 pages
Scientific paper
We consider four (real or complex) dimensional hyper-K\"ahler 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.
Dunajski Maciej
Tod Paul
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