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arxiv: math/9911121 · v1 · submitted 1999-11-16 · 🧮 math.DG · gr-qc· math-ph· math.MP· nlin.SI· solv-int

Einstein metrics, hypercomplex structures and the Toda field equation

classification 🧮 math.DG gr-qcmath-phmath.MPnlin.SIsolv-int
keywords metricseinsteinequationfieldhypercomplexsolutionstodaadmit
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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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