English

On an Enneper-Weierstrass-type representation of constant Gaussian curvature surfaces in $3$-dimensional hyperbolic space

Differential Geometry 2014-04-22 v1

Abstract

For all k]0,1[k\in]0,1[, we construct a canonical bijection between the space of ramified coverings of the sphere and the space of complete immersed surfaces in 33-dimensional hyperbolic space of finite area and of constant extrinsic curvature equal to kk. We show, furthermore, that this bijection restricts to a homeomorphism over each stratum of the space of ramified coverings of the sphere.

Keywords

Cite

@article{arxiv.1404.5006,
  title  = {On an Enneper-Weierstrass-type representation of constant Gaussian curvature surfaces in $3$-dimensional hyperbolic space},
  author = {Graham Smith},
  journal= {arXiv preprint arXiv:1404.5006},
  year   = {2014}
}