A Note on Riemannian Anti-self-dual Einstein metrics with Symmetry
نویسنده
چکیده
We give a complete proof of the result stated in [1], that the general Einstein metric with a symmetry, an anti-self-dual Weyl tensor and nonzero scalar curvature is determined by a solution of the SU(∞)Toda field equation. We consider the two canonical forms found for solutions to the same problem by Przanowski [2] and show that his Class A will reduce to the Toda equation with respect to a second complex structure, different from that in which the metric is first given.
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