Constant Angle Surfaces in $\H^2\times \R$

TL;DR

This paper classifies surfaces in the hyperbolic plane times the real line where the angle with a fixed direction remains constant, providing a comprehensive understanding of their geometric properties.

Contribution

It offers the first complete classification of constant angle surfaces in the product space  R, expanding the understanding of their geometry.

Findings

Complete classification of constant angle surfaces in  R

Identification of geometric properties unique to these surfaces

Foundation for further studies in hyperbolic product spaces

Abstract

In this paper we classify constant angle surfaces in $\H^2\times\R$, where $\H^2$ is the hyperbolic plane.