Survey on real forms of the complex A2(2)-Toda equation and surface theory

Abstract

The classical result of describing harmonic maps from surfaces into symmetric spaces of reductive Lie groups [9] states that the Maurer-Cartan form with an additional parameter, the so-called loop parameter, is integrable for all values of the loop parameter. As a matter of fact, the same result holds for k-symmetric spaces over reductive Lie groups, [8].

Keywords

• minimal lagrangian surfaces
• affine spheres
• loop groups
• real forms
• tzitzéica equations
• primary 53a10
• 53b30
• 58d10
• secondary 53c42