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arXiv · 1903.11841

Spaces of locally homogeneous affine surfaces

Miguel Brozos-Vázquez·Eduardo García-Río·Peter Gilkey
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Abstract

We examine the topology of various spaces of locally homogeneous affine manifolds which arise from the classification result of Opozda [B. Opozda, A classification of locally homogeneous connections on 2-dimensional manifolds, Differential Geom. Appl. 21 (2004), 173-198.] as orbits of the action of $GL(2,\mathbb{R})$ (Type $\mathcal{A}$) and the $ax+b$ group (Type $\mathcal{B}$). We determine the topology of the spaces of Type $\mathcal{A}$ models in relation to the rank of the Ricci tensor. We determine the topology of the spaces of Type $\mathcal{B}$ models which either are flat or where the Ricci tensor is alternating.

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Miguel Brozos-Vázquez, Eduardo García-Río, Peter Gilkey. 2019-03-28. Spaces of locally homogeneous affine surfaces. https://arxiv.org/abs/1903.11841

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