Constant angle surfaces in the Lorentzian Heisenberg group

TL;DR

This paper characterizes and explicitly parametrizes constant angle spacelike and timelike surfaces in the Lorentzian Heisenberg group, providing new insights into their geometric structure with concrete examples.

Contribution

It introduces a detailed characterization and explicit parametrization of constant angle surfaces in the Lorentzian Heisenberg group, including examples.

Findings

Explicit local parametrizations of constant angle surfaces

Classification of spacelike and timelike cases

Examples illustrating the geometric properties

Abstract

In this paper, we define and, then, we characterize constant angle spacelike and timelike surfaces in the three-dimensional Heisenberg group, equipped with a 1-parameter family of Lorentzian metrics. In particular, we give an explicit local parametrization of these surfaces and we produce some examples.