A characterization of Weingarten surfaces in hyperbolic 3-space

摘要

We study 2-dimensional submanifolds of the space ${mathbb{L}}({mathbb{H}}^{3})$ of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral Kähler structure. Such a surface is Lagrangian iff there exists a surface in ℍ3 orthogonal to the geodesics of Σ.