# Constant curvature translation surfaces in Galilean 3-space

## TL;DR

This paper classifies five types of translation surfaces in Galilean 3-space, analyzing their curvature properties based on the planarity of generating curves and the absolute figure.

## Contribution

It introduces a complete classification of translation surfaces in Galilean 3-space, detailing their curvature characteristics depending on the planarity of the generating curves.

## Key findings

- Five types of translation surfaces identified in Galilean 3-space.
- Most surfaces have arbitrary constant Gaussian and mean curvature.
- Explicit curvature properties depend on the planarity of the generating curves.

## Abstract

Total five different types of translation surfaces, based upon planarity of translating curves and the absolute figure, arise in a Galilean 3-space. Excepting the type in which both of translating curves are non-planar we obtain these surfaces with arbitrary constant Gaussian and mean curvature.