Hyperbolic constant mean curvature one surfaces: Spinor representation and trinoids in hypergeometric functions
Differential Geometry
2007-05-23 v2
Abstract
We present a global representation for surfaces in 3-dimensional hyperbolic space with constant mean curvature 1 (CMC-1 surfaces) in terms of holomorphic spinors. This is a modification of Bryant's representation. It is used to derive explicit formulas in hypergeometric functions for CMC-1 surfaces of genus 0 with three regular ends which are asymptotic to catenoid cousins (CMC-1 trinoids).
Cite
@article{arxiv.math/0206021,
title = {Hyperbolic constant mean curvature one surfaces: Spinor representation and trinoids in hypergeometric functions},
author = {Alexander I. Bobenko and Tatyana V. Pavlyukevich and Boris A. Springborn},
journal= {arXiv preprint arXiv:math/0206021},
year = {2007}
}
Comments
29 pages, 9 figures. v2: figures of cmc1-surfaces corrected