Canonical Coordinates and Principal Directions for Surfaces in $\H^2\times\R$

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. Some examples are given to complete the study.

arXiv comment25 Latex pages, to appear in Taiwanese Mathematical Journal

References in corpus (3)

• Constant angle surfaces in the Heisenberg group
• On a class of hypersurfaces in $\Sf^n\times \R$ and $\Hy^n\times \R$
• Hypersurfaces with constant sectional curvature of $\Sf^n\times \R$ and $\Hy^n\times \R$