The geometry of the Toda equation

Details The geometry of the Toda equation The geometry of the Toda equation

1999-08-30

arxiv.org/abs/math/9908164v2

J. Geom. Phys. 36 (2000) 152-162

Mathematics

Differential Geometry

AMS-LaTeX 11 pages; minor changes to title, keywords and references

Scientific paper

10.1016/S0393-0440(00)00019-X

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.

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