The index of the pseudo-Riemannian Dirac operator as a transversally Elliptic operator (Q791222)
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scientific article; zbMATH DE number 3850151
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The index of the pseudo-Riemannian Dirac operator as a transversally Elliptic operator |
scientific article; zbMATH DE number 3850151 |
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The index of the pseudo-Riemannian Dirac operator as a transversally Elliptic operator (English)
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1983
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Let \((M^ n,g)\) be an n-dimensional closed space- and time- orientable pseudo-Riemannian spin manifold and let G be a compact group of orientation-preserving isometries on (M,g). If there are no isotropic directions transversal to the orbits of G, then the Dirac operator D on (M,g) is transversally elliptic. We prove that the index of D vanishes. Furthermore, if g has odd index, then the spinor-index of \((M^{2m},g)\) vanishes.
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Dirac operator
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pseudo-Riemannian spin manifold
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isotropic directions
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spinor-index
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0.7506651282310486
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0.7506651282310486
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0.7503504753112793
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0.7467915415763855
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