Dirac operators and the Weitzenböck formula for \(\text{Spin}^G(3)\)-structures (Q2770393)
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scientific article; zbMATH DE number 1703225
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dirac operators and the Weitzenböck formula for \(\text{Spin}^G(3)\)-structures |
scientific article; zbMATH DE number 1703225 |
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28 April 2002
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spinor
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connection
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curvature
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Dirac operator
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Dirac operators and the Weitzenböck formula for \(\text{Spin}^G(3)\)-structures (English)
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In this paper the author presents a few properties of the Dirac operators associated to Spin\(^{G}(3)\)-structures and gives a generalised version of the Weitzenböck formula for Spin\(^{G}(3)\)-structures, which has the following form NEWLINE\[NEWLINE D_A^2=\nabla_{\widehat A}^{*}\nabla_{\widehat A}+\tfrac{1}{4}s+\Gamma(F_A), NEWLINE\]NEWLINE where \(\nabla_{\widehat A}\) is the connection induced by a connection 1-form \(A\) on an \(SO(3)\)-principal bundle, \(F_A\) its curvature and \(s\) the scalar curvature.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00064].
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0.759588897228241
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0.7593986392021179
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0.7564002871513367
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0.7444148659706116
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