A classification of locally homogeneous affine connections on compact surfaces
Differential Geometry
2016-03-09 v1
Abstract
We classify the affine connections on compact orientable surfaces for which the pseudogroup of local isometries acts transitively. We prove that such a connection is either torsion-free and flat, the Levi-Civita connection of a Riemannian metric of constant curvature or the quotient of a translation-invariant connection in the plane.
Keywords
Cite
@article{arxiv.1404.5249,
title = {A classification of locally homogeneous affine connections on compact surfaces},
author = {Adolfo Guillot and Antonia Sánchez Godinez},
journal= {arXiv preprint arXiv:1404.5249},
year = {2016}
}