Cocalibrated \(G_2\)-manifolds with Ricci flat characteristic connection (Q2844465)
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scientific article; zbMATH DE number 6202721
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cocalibrated \(G_2\)-manifolds with Ricci flat characteristic connection |
scientific article; zbMATH DE number 6202721 |
Statements
28 August 2013
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cocalibrated \(G_2\)-manifolds
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connections with torsion
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parallel vector fields
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math.DG
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math-ph
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math.MP
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0.88895595
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0.87359387
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0.87131965
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Cocalibrated \(G_2\)-manifolds with Ricci flat characteristic connection (English)
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In this article, \(7\)-dimensional cocalibrated \(G_2\)-manifolds \(M\) are studied. Any such manifold admits a unique connection \(\nabla\) with skew-symmetric torsion and \(\nabla\)-parallel spinor field. The author considers the special case when the \(\nabla\)-Ricci tensor vanishes and investigates the geometry of these manifolds when there are three \(\nabla\)-parallel vector fields or two special \(\nabla\)-parallel vector fields. Classifications are given under additional assumptions.
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