Trace formulae for \(S^ 1\) invariant Green's operators on \(S^ 2\) (Q1360928)
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scientific article; zbMATH DE number 1038297
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Trace formulae for \(S^ 1\) invariant Green's operators on \(S^ 2\) |
scientific article; zbMATH DE number 1038297 |
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Trace formulae for \(S^ 1\) invariant Green's operators on \(S^ 2\) (English)
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12 March 1998
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The author studies the spectrum of the Laplacian acting on 1-forms for a surface of revolution diffeomorphic to \(S^2\) and obtains for the \(S^1\)-invariant spectrum a trace formula in terms of the eigenvalues of its Green operator. Then this trace formula is used for the determination of the negative scalar curvature of the initial manifold.
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\(S^ 1\)-invariant spectrum
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spectrum
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Laplacian
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trace formula
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Green operator
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negative scalar curvature
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