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arXiv · 0912.0169

Classification of compact homogeneous spaces with invariant $G_2$-structures

Hong Van Le·Mobeen Munir
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Abstract

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).

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Hong Van Le, Mobeen Munir. 2009-12-01. Classification of compact homogeneous spaces with invariant $G_2$-structures. https://arxiv.org/abs/0912.0169

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