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ON COMPACT HOMOGENEOUS $\mathbf{\text{G}_{2(2)}}$ -MANIFOLDS



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 $\text{G}_{2(2)}$ -structure.



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Wolfgang Globke is supported by the Austrian Science Fund FWF grant I 3248.



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