Asian Journal of Mathematics

Volume 21 (2017)

Number 2

Dressing actions on proper definite affine spheres

Pages: 363 – 390

DOI: http://dx.doi.org/10.4310/AJM.2017.v21.n2.a6

Authors

Zhicheng Lin (Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, Hubei, China)

Gang Wang (Department of Mathematics, Shandong University, Jinan, Shandong, China)

Erxiao Wang (Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

Abstract

We will first clarify the loop group formulations for both hyperbolic and elliptic definite affine spheres in $\mathbb{R}^3$. 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.

Keywords

definite affine sphere, Tzitzeica equation, dressing action, Monge–Ampère equation

2010 Mathematics Subject Classification

35Q35, 37K25, 53A15

Full Text (PDF format)

Received 16 August 2015

Published 5 July 2017