Nondegeneracy of the eigenvalues of the Hodge Laplacian for generic metrics on 3-manifolds (Q2841350)
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scientific article; zbMATH DE number 6191310
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nondegeneracy of the eigenvalues of the Hodge Laplacian for generic metrics on 3-manifolds |
scientific article; zbMATH DE number 6191310 |
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Nondegeneracy of the eigenvalues of the Hodge Laplacian for generic metrics on 3-manifolds (English)
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25 July 2013
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Hodge Laplacian
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Beltrami operator
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generic metrics
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three-dimensional manifold
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Let \(M\) be a compact three-dimensional Riemannian manifold and \(r\geq 2.\) It is the main result of the paper that there is a residual subset \(\Gamma\) of the space of \(C^r\)-metrics such that, for all \(g\in \Gamma,\) the following holds: The non-zero eigenvalues of the Hodge Laplacian \(\Delta_g\) on \(p\)-forms have multiplicity \(1\) for \(0 \leq p\leq 3\) and the zero set of eigenforms of degree \(p=1,2\) are isolated. The authors use a detailed analysis of the Beltrami operator \(\star_g \circ d.\)
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