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

الأصل · EN

For all k∈]0,1[, we construct a canonical bijection between the space of ramified coverings of the sphere and the space of complete immersed surfaces in 3-dimensional hyperbolic space of finite area and of constant extrinsic curvature equal to k. We show, furthermore, that this bijection restricts to a homeomorphism over each stratum of the space of ramified coverings of the sphere.