Affine Killing vector fields on homogeneous surfaces with torsion
Differential Geometry
2019-07-17 v1 General Relativity and Quantum Cosmology
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.
Cite
@article{arxiv.1906.01694,
title = {Affine Killing vector fields on homogeneous surfaces with torsion},
author = {Daniela D'Ascanio and Peter Gilkey and Pablo Pisani},
journal= {arXiv preprint arXiv:1906.01694},
year = {2019}
}