Dressing Actions on Proper Definite Affine Spheres

Abstract

We will first clarify the loop group formulations for both hyperbolic and elliptic definite affine spheres in R^3. Then we classify the rational elements with 3 poles or 6 poles in a real twisted loop group, and compute dressing actions of them on such surfaces. Some new examples with pictures will be produced at last.

References in corpus (1)

• Darboux transformations for two dimensional elliptic affine Toda equations

Cited by in corpus (1)

• The associated families of semi-homogeneous complete hyperbolic affine spheres