# Affine Killing vector fields on homogeneous surfaces with torsion

## TL;DR

This paper investigates how torsion influences affine Killing vectors on homogeneous surfaces, providing a complete classification of their Lie algebras, which aids in identifying non-metrizable surfaces in extended gravity theories.

## Contribution

It offers a comprehensive classification of affine Killing vector fields on homogeneous surfaces with torsion, advancing understanding of affine symmetries in extended gravitational models.

## Key findings

- Complete description of Lie algebras of affine Killing vectors
- Identification of conditions for non-metrizable surfaces
- Framework for analyzing torsion effects on symmetries

## Abstract

Many extensions of General Relativity are based on considering metric and affine structures as independent properties of spacetime. This leads to the possibility of introducing torsion as an independent degree of freedom. In this article we examine the effects of torsion on the affine Killing vectors of two-dimensional manifolds. We give a complete description of the Lie algebras of affine Killing vector fields on homogeneous surfaces. This can be used in the search of non-metrizable surfaces of interest.