Einstein metrics, hypercomplex structures and the Toda field equation

Details Einstein metrics, hypercomplex structures and the Toda field equation Einstein metrics, hypercomplex structures and the Toda field equation

1999-11-16

arxiv.org/abs/math/9911121v1

Differ.Geom.Appl. 14 (2001) 199-208

Mathematics

Differential Geometry

9 pages

Scientific paper

We obtain explicitly all solutions of the SU(infinity) Toda field equation with the property that the associated Einstein-Weyl space admits a 2-sphere of divergence-free shear-free geodesic congruences. The solutions depend on an arbitrary holomorphic function and give rise to new hyperKahler and selfdual Einstein metrics with one dimensional isometry group. These metrics each admit a compatible hypercomplex structure with respect to which the symmetries are triholomorphic.

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