The geometry of the Toda equation

JOURNAL OF GEOMETRY AND PHYSICS

卷:36

Article

Calderbank, DMJ

关键词: Toda equation;    Einstein-Weyl geometry;   

DOI  :  10.1016/S0393-0440(00)00019-X

来源: Elsevier

【 摘 要 】

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. (C) 2000 Elsevier Science B.V. All rights reserved. MSG: 53A303 53C25.

【 授权许可】

Free