On the Geometry of Constant Angle Surfaces in $Sol_3$

TL;DR

This paper classifies all surfaces in the 3D Lie group $Sol_3$ with normals forming a constant angle with a specific invariant vector field, enhancing understanding of their geometric properties.

Contribution

It provides a complete classification of constant angle surfaces in $Sol_3$, a problem previously unexplored in this context.

Findings

Complete classification of constant angle surfaces in $Sol_3$

Identification of geometric properties of these surfaces

Extension of constant angle surface theory to Lie groups

Abstract

In this paper we classify all surfaces in the 3-dimensional Lie group $Sol_3$ whose normals make constant angle with a left invariant vector field.