Hyperbolic constant mean curvature one surfaces: Spinor representation and trinoids in hypergeometric functions

Details Hyperbolic constant mean curvature one surfaces: Spinor representation and trinoids in hypergeometric functions Hyperbolic constant mean curvature one surfaces: Spinor representation and trinoids in hypergeometric functions

2002-06-04

arxiv.org/abs/math/0206021v2

Math. Z. 245, 63--91(2003)

Mathematics

Differential Geometry

29 pages, 9 figures. v2: figures of cmc1-surfaces corrected

Scientific paper

10.1007/s00209-003-0511-5

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).

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