Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space
It is well known that the Weierstrass-Enneper representation formula plays an important role in the theory of minimal surfaces in Euclidean space \(E^3\). In 1979, K. Kenmotsu gave a representation formula for surfaces with non-zero constant mean curvature in Euclidean space \(E^3\). In this paper, the authors obtain a hyperbolic version of the result due to Kenmotsu. That is, they derive a representation formula for surfaces in the hyperbolic space \(H^3(-c)\) with constant mean curvature \(0<H<c\). It is necessary to point out that \textit{R. Bryant} [Astérisque 154-155, 321-347 (1988; Zbl 0635.53047)] gave the representation formula for surfaces in the hyperbolic space \(H^3(-c)\) with constant mean curvature \(c\).
scientific article; zbMATH DE number 1553007