A comparison theorem for eigenvalues of the covariant Laplacian (Q753228)
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scientific article; zbMATH DE number 4180380
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A comparison theorem for eigenvalues of the covariant Laplacian |
scientific article; zbMATH DE number 4180380 |
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A comparison theorem for eigenvalues of the covariant Laplacian (English)
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1990
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The minimax principle is employed to bound the eigenvalues \(\lambda_ n\), of a covariant Laplacian associated to a connection on a vector bundle, above by the eigenvalues \(\mu_ n\), of a corresponding scalar Laplacian. If there exists a non-vanishing eigensection, of the bundle, and \(n=0\), then equality is attained. Some examples are given.
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Riemannian manifold
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minimax principle
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eigenvalues
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covariant Laplacian
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connection
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vector bundle
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0.91409177
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0.91027206
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0.9026178
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