The geometry of the Toda equation

✍ Scribed by David M.J. Calderbank

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 86 KB
• Volume: 36
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(00)00019-x

✦ Synopsis

I show that solutions of the SU(∞) 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.