Harmonic superconformal maps of surfaces in Hn

✍ Scribed by Eduardo Hulett

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 198 KB
• Volume: 42
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(01)00082-1

✦ Synopsis

The class of harmonic superconformal maps from Riemann surfaces into real hyperbolic spaces is considered and harmonic sequences are constructed for these maps. They are used to obtain a rigidity result for such maps and to construct primitive lifts into an auxiliary flag space F m . It is also shown that superconformal harmonic maps into H 2m and H 2m-1 are locally described by 2D-affine Toda fields associated to the pair (so(2m+1, C), σ ), where σ is the involution determined by the non-compact real form so(1, 2m). Applying the Adler-Kostant-Symes integration scheme to appropriate loop algebras we construct finite type primitive maps ψ : H 2 → F m , and harmonic superconformal maps f : H 2 → H 2m and hence finite type Toda fields.