# Constant angle surfaces in the Heisenberg group

## TL;DR

This paper extends the concept of constant angle surfaces to a broad class of three-dimensional homogeneous spaces, providing a classification in the Heisenberg group and revealing their constant Gaussian curvature.

## Contribution

It generalizes constant angle surfaces to Bianchi-Cartan-Vranceanu spaces and offers a complete local classification in the Heisenberg group.

## Key findings

- Constant angle surfaces have constant Gaussian curvature.
- Complete local classification in the Heisenberg group.
- Extension of the concept to general homogeneous spaces.

## Abstract

In this article we generalize the notion of constant angle surfaces in S^2 x R and H^2 x R to general Bianchi-Cartan-Vranceanu spaces, i.e. essentially to three-dimensional homogeneous spaces with a four-dimensional isometry group. We show that these surfaces have constant Gaussian curvature and we give a complete local classification in the Heisenberg group.