Transitive group actions and Ricci curvature properties (Q1123418)
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scientific article; zbMATH DE number 4109560
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Transitive group actions and Ricci curvature properties |
scientific article; zbMATH DE number 4109560 |
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Transitive group actions and Ricci curvature properties (English)
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1988
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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.
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group of isometries
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non-negative Ricci curvature
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homogeneous Riemannian manifold
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