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

Part of: Global differential geometry

Published online by Cambridge University Press:  04 September 2019

WOLFGANG GLOBKE Open the ORCID record for WOLFGANG GLOBKE [Opens in a new window]
WOLFGANG GLOBKE*
Affiliation:
Faculty of Mathematics, Oskar-Morgenstern-Platz 1, Universität Wien, 1090Vienna, Austria
*
e-mail: wolfgang.globke@univie.ac.at
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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 $\text{G}_{2(2)}$-structure.

Keywords

G2(2) holonomycompact homogeneous spacespseudo-Riemannian manifolds

MSC classification

Primary: 53C50: Lorentz manifolds, manifolds with indefinite metrics
Secondary: 53C30: Homogeneous manifolds 53C29: Issues of holonomy
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 110 , Issue 1 , February 2021 , pp. 71 - 80
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Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by M. Murray

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

References

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