The geometry of the Toda equation
Differential Geometry
2009-10-31 v2 Mathematical Physics
math.MP
Abstract
I show that solutions of the SU(infinity) Toda field equation generating a fixed Einstein-Weyl space are governed by a linear equation on the Einstein-Weyl space. From this, obstructions to the existence of Toda solutions generating a given Einstein-Weyl space are found. I also give a classification of Einstein-Weyl spaces arising from the Toda equation in more than one way. This classification coincides with a class of spaces found by Ward and hence clarifies some of their properties. I end by discussing the simplest examples.
Cite
@article{arxiv.math/9908164,
title = {The geometry of the Toda equation},
author = {David M. J. Calderbank},
journal= {arXiv preprint arXiv:math/9908164},
year = {2009}
}
Comments
AMS-LaTeX 11 pages; minor changes to title, keywords and references