A Note on Riemannian Anti-self-dual Einstein metrics with Symmetry
High Energy Physics - Theory
2007-05-23 v1
Abstract
We give a complete proof of the result stated in an earlier article, 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 -Toda field equation. We consider the two canonical forms found for solutions to the same problem by Przanowski (J.Math.Phys. 32(1991) 1004-1010) 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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Cite
@article{arxiv.hep-th/0609071,
title = {A Note on Riemannian Anti-self-dual Einstein metrics with Symmetry},
author = {Paul Tod},
journal= {arXiv preprint arXiv:hep-th/0609071},
year = {2007}
}
Comments
9 pages