The Dirac spectrum of Bieberbach manifolds (Q5931240)
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scientific article; zbMATH DE number 1590742
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Dirac spectrum of Bieberbach manifolds |
scientific article; zbMATH DE number 1590742 |
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The Dirac spectrum of Bieberbach manifolds (English)
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30 April 2002
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Dirac operator
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Bieberbach manifolds
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eta invariant
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parallel spinors
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spectrum
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Bieberbach manifolds are complete Riemannian manifolds with vanishing curvature. NEWLINENEWLINENEWLINEIn the present paper explicit formulas for the eigenvalues of the Dirac operator on three-dimensional compact Bieberbach manifolds are derived for all spin structures. The corresponding \(\eta\)-invariants are computed. From the results it also follows that the flat torus is the only compact three-dimensional spin manifold carrying a non-zero parallel spinor.
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