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ON COMPACT HOMOGENEOUS $\mathbf{\text{G}_{2(2)}}$-MANIFOLDS
Published online by Cambridge University Press: 04 September 2019
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 $\text{G}_{2(2)}$-structure.
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- Research Article
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- © 2019 Australian Mathematical Publishing Association Inc.
Footnotes
Communicated by M. Murray
Wolfgang Globke is supported by the Austrian Science Fund FWF grant I 3248.