Classification of compact homogeneous spaces with invariant $G_2$-structures
| Autor: | Van Le, Hong, Munir, Mobeen |
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| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Advances in Geometry, 12(2012), 303-328 |
| Druh dokumentu: | Working Paper |
| Popis: | In this note we classify all homogeneous spaces $G/H$ admitting a $G$-invariant $G_2$-structure, assuming that $G$ is a compact Lie group and $G$ acts effectively on $G/H$. They include a subclass of all homogeneous spaces $G/H$ with a $G$-invariant $\tilde G_2$-structure, where $G$ is a compact Lie group. There are many new examples with nontrivial fundamental group. We study a subclass of homogeneous spaces of high rigidity and low rigidity and show that they admit families of invariant coclosed $G_2$-structures (resp. $\tilde G_2$-structures). Comment: final version, 24p |
| Databáze: | arXiv |
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