Classification of compact homogeneous spaces with invariant G\(_2\)-structures (Q2882935)
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scientific article; zbMATH DE number 6033007
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classification of compact homogeneous spaces with invariant G\(_2\)-structures |
scientific article; zbMATH DE number 6033007 |
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11 May 2012
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compact homogeneous spaces
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\(G_2\)-structure
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invariant 3-forms
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0.92908645
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0.92348146
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0.91958094
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0.9195809
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0.8970626
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0.8948399
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Classification of compact homogeneous spaces with invariant G\(_2\)-structures (English)
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Let \(G\) be a connected compact Lie group. The authors classify all \(7\)-dimensional homogeneous spaces \(M = G/H\) (not necessary simply connected) which admit an invariant \(G_2\)-structure, where \(G_2\) is the exceptional compact or non compact simple Lie group. They determine for each homogeneous space the dimension of the space of invariant \(G_2\)-structures, which is equal to the dimension of the space of isotropy invariant 3-forms in the tangent space \(T_x(G/H)\). New families of invariant coclosed \(G_2\)-structures are constructed.
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