New spectral characterization theorems for \(S^ 2\) (Q749882)
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scientific article; zbMATH DE number 4173816
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New spectral characterization theorems for \(S^ 2\) |
scientific article; zbMATH DE number 4173816 |
Statements
New spectral characterization theorems for \(S^ 2\) (English)
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1991
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Two theorems are proved: 1) Among surfaces of revolution which are diffeomorphic to \(S^ 2\), the constant curvature metric is completely characterized by the multiplicities of its eigenvalues and, 2) If the square of an eigenfunction is, again, an eigenfunction then the metric is the standard metric on \(S^ 2\).
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Laplacian
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spectrum
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surfaces of revolution
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constant curvature metric
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eigenvalues
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