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arXiv · 1512.05515

Homogeneous affine surfaces: affine Killing vector fields and Gradient Ricci solitons

M. Brozos-Vázquez·E. García-Río·P. Gilkey
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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.

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M. Brozos-Vázquez, E. García-Río, P. Gilkey. 2015-12-17. Homogeneous affine surfaces: affine Killing vector fields and Gradient Ricci solitons. https://arxiv.org/abs/1512.05515

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