Homogeneous affine surfaces: affine Killing vector fields and Gradient Ricci solitons
Differential Geometry
2015-12-18 v1
Abstract
The homogeneous affine surfaces have been classified by Opozda. They may be grouped into 3 families, which are not disjoint. The connections which arise as the Levi-Civita connection of a surface with a metric of constant Gauss curvature form one family; there are, however, two other families. For a surface in one of these other two families, we examine the Lie algebra of affine Killing vector fields and we give a complete classification of the homogeneous affine gradient Ricci solitons. The rank of the Ricci tensor plays a central role in our analysis.
Keywords
Cite
@article{arxiv.1512.05515,
title = {Homogeneous affine surfaces: affine Killing vector fields and Gradient Ricci solitons},
author = {M. Brozos-Vázquez and E. García-Río and P. Gilkey},
journal= {arXiv preprint arXiv:1512.05515},
year = {2015}
}