The harmonic field of a Riemannian manifold (Q2444675)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The harmonic field of a Riemannian manifold |
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The harmonic field of a Riemannian manifold (English)
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10 April 2014
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In the paper under review the author uses Sullivan's construction of minimal models for topological spaces for the case of simply connected closed Riemannian manifolds \((M,<\,,\,>)\) to define a unique finitely generated field extension \(\mathbf{k}\) of \(\mathbb{Q}\), the harmonic field of \((M,<\,,\,>)\) and a morphism, \(m: (\Lambda V,d)\to A_{DR}(M)\), from the Sullivan model defined over \(\mathbf{k}\). The Sullivan model and the morphism are determined up to isomorphism. Examples are constructed to show that every finitely generated extension field of \(\mathbb{Q}\) occurs as a harmonic field of such a Riemannian manifold.
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harmonic field
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Riemannian manifold
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Sullivan model
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