Spaces of locally homogeneous affine surfaces

Abstract

We examine the topology of various spaces of locally homogeneous affine manifolds which arise from the classification result of Opozda [11] as orbits of the action of GL(2, R) (Type A) and the ax + b group (Type B). We determine the topology of the spaces of Type A models in relation to the rank of the Ricci tensor. We determine the topology of the spaces of Type B models which either are flat or where the Ricci tensor is alternating.2010 Mathematics Subject Classification. 53A15, 53C05, 53B05.