On Distinguished local coordinates for locally homogeneous affine surfaces
Differential Geometry
2019-01-14 v1
Abstract
We give a new short self-contained proof of the result of Opozda [B. Opozda, A classification of locally homogeneous connections on 2-dimensional manifolds, Differential Geom. Appl. 21 (2004), 173-198.] classifying the locally homogeneous torsion free affine surfaces and the extension to the case of surfaces with torsion due to Arias-Marco and Kowalski [T. Arias-Marco and O. Kowalski, Classification of locally homogeneous linear connections with arbitrary torsion on 2-dimensional manifolds, Monatsh. Math. 153 (2008), 1-18.]. Our approach rests on a direct analysis of the affine Killing equations and is quite different than the approaches taken previously in the literature.
Cite
@article{arxiv.1901.03523,
title = {On Distinguished local coordinates for locally homogeneous affine surfaces},
author = {M. Brozos-Vázquez and E. García-Río and P. Gilkey},
journal= {arXiv preprint arXiv:1901.03523},
year = {2019}
}