CANONICAL COORDINATES AND PRINCIPAL DIRECTIONS FOR SURFACES IN $\mathbb{H}^2 × \mathbb{R}$

Abstract

In this paper we characterize and classify surfaces in ${\mathbb{H}}^2\times{\mathbb{R}}$ which have a canonical principal direction. Here ${\mathbb{H}}^2$ denotes the hyperbolic plane. We study some geometric properties such as minimality and flatness. Several examples are given to complete the study.