Isospectral flat Klein bottles (Q2760689)
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scientific article; zbMATH DE number 1682231
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Isospectral flat Klein bottles |
scientific article; zbMATH DE number 1682231 |
Statements
13 December 2001
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isospectral manifolds
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isometric Riemann surfaces
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eigenvalues of the Laplacian
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Isospectral flat Klein bottles (English)
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The author proves that two Klein bottles are isometric if and only if they are isospectral. The proof is based on an explicit formula for the trace function on a Klein bottle. The formula is obtained from the connection of the spectra of the Laplacian on a Klein bottle and its covering torus, with the trace formula for a torus previously found by \textit{R.~Brooks} [Am. Math. Mon. 95, No. 9, 823-839 (1988; Zbl 0673.58046)].
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