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

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 13 references

Metrics of constant curvature 1 with three conical singularities on the 2-sphere

M. Umehara, K. Yamada
Illinois J. Math., • 2000

A criterion for the existence of a parabolic stable bundle of rank two over the projective line

Bo A. I. Bobenko
Int . Journal of Math . • 1998

A criterion for the existence of a parabolic stable bundle of rank two over the projective line, Int

I. Biswas
Journal of Math • 1998

Surfaces of constant mean curvature c in H3(−c2) with prescribed hyperbolic Gauss map, Math. Ann

M. Umehara, K. Yamada
1996

Complete surfaces of constant mean curvature-1 in the hyperbolic 3-space

M. Umehara, K. Yamada
Ann. of Math., • 1993

Surfaces of constant mean curvature c in H 3 ( − c 2 ) with prescribed hyperbolic Gauss map

M. Umehara, K. Yamada
Math . Ann . • 1993