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 , we construct a canonical bijection between the space of ramified coverings of the sphere and the space of complete immersed surfaces in -dimensional hyperbolic space of finite area and of constant extrinsic curvature equal to . 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}
}