Transitive group actions and Ricci curvature properties
The main results in this paper are: (i) Any transitive group of isometries of a homogeneous Riemannian manifold with non-negative Ricci curvature is unimodular. In fact, there is a structural splitting theorem for such groups. (ii) Any transitive connected unimodular group of isometries of a homogeneous Riemannian manifold with negative Ricci curvature is semi-simple and closed. These results extend known results by J. Milnor and J. Wolf.
scientific article; zbMATH DE number 4109560