Symmetric affine surfaces with torsion
Differential Geometry
2020-01-08 v1 General Relativity and Quantum Cosmology
Abstract
We study symmetric affine surfaces which have non-vanishing torsion tensor. We give a complete classification of the local geometries possible if the torsion is assumed parallel. This generalizes a previous result of Opozda in the torsion free setting; these geometries are all locally homogeneous. If the torsion is not parallel, we assume the underlying surface is locally homogeneous and provide a complete classification in this setting as well.
Cite
@article{arxiv.1910.10028,
title = {Symmetric affine surfaces with torsion},
author = {Daniela D'Ascanio and Peter Gilkey and Pablo Pisani},
journal= {arXiv preprint arXiv:1910.10028},
year = {2020}
}