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arXiv · 1808.10160

On compact homogeneous $\mathrm{G}_{2(2)}$-manifolds

Wolfgang Globke
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Abstract

We prove that among all compact homogeneous spaces for an effective transitive action of a Lie group whose Levi subgroup has no compact simple factors, the seven-dimensional flat torus is the only one that admits an invariant torsion-free $\mathrm{G}_{2(2)}$-structure.

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Wolfgang Globke. 2018-08-30. On compact homogeneous $\mathrm{G}_{2(2)}$-manifolds. https://doi.org/10.1017/s1446788719000296

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