Comparison of metrics on three-dimensional Lie groups (Q1192781)
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scientific article; zbMATH DE number 61684
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Comparison of metrics on three-dimensional Lie groups |
scientific article; zbMATH DE number 61684 |
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Comparison of metrics on three-dimensional Lie groups (English)
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27 September 1992
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The local equivalence of left-invariant metrics with the same curvature on three-dimensional Lie groups \(G_ 1\) and \(G_ 2\) (where \(G_ 1\) is unimodular and \(G_ 2\) is non-unimodular) is studied. A necessary and sufficient condition for these metrics to be locally equivalent is given. From this result follows the existence of homogeneous Riemannian manifolds which have the same curvature, but are not locally isometric.
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Singer invariant
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left-invariant metrics
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0.8310608267784119
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