Uniqueness and non-existence of metrics with prescribed Ricci curvature (Q760921)
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scientific article; zbMATH DE number 3886686
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniqueness and non-existence of metrics with prescribed Ricci curvature |
scientific article; zbMATH DE number 3886686 |
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Uniqueness and non-existence of metrics with prescribed Ricci curvature (English)
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1984
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The authors give conditions under which the Ricci tensor uniquely determines the underlying Levi-Civita connection and find restrictions on a doubly covariant tensor to be the Ricci tensor of some Riemannian metric. The results extend a result of R. Hamilton who showed that the standard metric on \(S^ n\) is uniquely determined by its Ricci tensor [see The Ricci curvature equation, preprint, MSRI (1983)].
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Ricci tensor
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Levi-Civita connection
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