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Uniqueness and non-existence of metrics with prescribed Ricci curvature. (English) Zbl 0556.53026

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)].
Reviewer: G.Thorbergsson

MSC:

53C20 Global Riemannian geometry, including pinching
53B20 Local Riemannian geometry
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References:

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