# Affine Factorable Surfaces in Pseudo-Galilean Space

## TL;DR

This paper investigates affine factorable surfaces of the second kind in pseudo-Galilean space, deriving their fundamental forms and curvatures, and classifies these surfaces based on their curvature properties.

## Contribution

It provides a classification of affine factorable surfaces in pseudo-Galilean space with explicit curvature conditions, using invariant theory and differential equations.

## Key findings

- Derived fundamental forms, Gaussian and mean curvatures of the surfaces.
- Classified surfaces with zero and non-zero Gaussian and mean curvatures.
- Presented examples illustrating the theoretical results.

## Abstract

An affine factorable surface of the second kind in the three dimensional pseudo-Galilean space G13 is studied depending on the invariant theory and theory of differential equation. The first and second fundamental forms, Gaussian curvature and mean curvature of the meant surface are obtained according to the basic principles of differential geometry. Also, some special cases are presented by changing the partial differential equation into the ordinary differential equation to simplify the solving process. The classification theorems of the considered surface with zero and non zero Gaussian and mean curvatures are given. Some examples of such a study are provided