Classification of isometric immersions of the hyperbolic space \(H^ 2\) into \(H^ 3\) (Q678576)

\textit{J. Hano} and \textit{K. Nomizu} [Math. Ann. 262, 245-253 (1983; Zbl 0507.53042)] studied isometric immersions of the hyperbolic plane into the Lorentz-Minkowski space. For complete spacelike convex surfaces of Minkowski 3-space, A.-M. Li gave a classification under certain conditions. In this paper, the authors give the classification of isometric immersions of the hyperbolic space \(H^2\) into \(H^3\) which possess bounded principal curvatures. For this they solve an elliptic Monge-Ampère equation on the unit disc.