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Why can't a Lie group act transitively on a finite volume hyperbolic manifold?
In the comments on the MathSE question "Is Seifert-Weber space homogeneous for a Lie group?",
it is claimed that if $ M $ is a manifold which admits a finite volume hyperbolic metric (...
- 4,081
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Examples of the Thurston geometries with transitive Lie group action
Here are some examples of compact homogeneous 3 manifolds for different Thurston geometries:
(1) Spherical: $\mathbb{S}^3 \cong \mathrm{SU}_2$ modulo any finite subgroup
(2) Euclidean: 3 torus $\...
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