Standard locally homogeneous spaces are classified by when their discrete groups are rigid, deform to nonstandard groups, or deform to Zariski-dense subgroups.
Benoist,Actions propres sur les espaces homogènes réductifs, Ann
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Deformations of Standard Locally Homogeneous Spaces
Standard locally homogeneous spaces are classified by when their discrete groups are rigid, deform to nonstandard groups, or deform to Zariski-dense subgroups.