J un 2 00 2 Hyperbolic constant mean curvature one surfaces : Spinor representation and trinoids in hypergeometric functions

@inproceedings{Bobenko2002JU2,
title={J un 2 00 2 Hyperbolic constant mean curvature one surfaces : Spinor representation and trinoids in hypergeometric functions},
author={Alexander I. Bobenko and Tatyana V. Pavlyukevich and Boris Springborn},
year={2002}
}

For minimal surfaces in R there is a representation, due to Weierstrass, in terms of holomorphic data. The Gauss-Codazzi equations for minimal surfaces in R are equivalent to those for surfaces in hyperbolic space with constant mean curvature 1 (CMC-1 surfaces). This lead Bryant [Br] to derive a representation for CMC-1 surfaces in terms of holomorphic data. The holomorphic data used in the Weierstrass representation for minimal surfaces consists alternatively of a function and a one-form, or… CONTINUE READING