Isometric Immersions of the Hyperbolic Plane into the Hyperbolic Space

摘要

In this paper, we parametrize the space of isometric immersions of thehyperbolic plane into the hyperbolic 3-space in terms of null-causal curves inthe space of oriented geodesics. Moreover, we characterize "ideal cones" (i.e.,cones whose vertices are on the ideal boundary) by behavior of their meancurvature.