Skip to main content Accessibility help
×
Home

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

  • WOLFGANG GLOBKE (a1)

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.

Copyright

Footnotes

Hide All

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

Footnotes

References

Hide All
[1] Baues, O., Globke, W. and Zeghib, A., ‘Isometry Lie algebras of indefinite homogeneous spaces of finite volume’, Proc. Lond. Math. Soc. 119(4) (2019), 11151148.
[2] Besse, A. L., Einstein Manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 10 (Springer, Berlin, 1987).
[3] Bonan, E., ‘Sur les variétés Riemanniennes à groupe d’holonomie G2 ou Spin(7)’, C. R. Math. Acad. Sci. Paris 262 (1966), 127129.
[4] Fino, A. and Luján, I., ‘Torsion-free G2(2) -structures with full holonomy on nilmanifolds’, Adv. Geom. 15(3) (2015), 381392.
[5] Globke, W. and Nikolayevsky, Y., ‘Compact pseudo-Riemannian homogeneous Einstein manifolds in low dimension’, Differential Geom. Appl. 54(Part B) (2017), 475489.
[6] Kath, I., ‘Nilpotent metric Lie algebras of small dimension’, J. Lie Theory 17 (2007), 4161.
[7] Kath, I., ‘Indefinite symmetric spaces with G2(2) -structure’, J. Lond. Math. Soc. 87(2) (2013), 853876.
[8] , H. V. and Munir, M., ‘Classification of compact homogeneous spaces with invariant G2 -structures’, Adv. Geom. 12(2) (2012), 303328.
[9] Leistner, T., Nurowski, P. and Sagerschnig, K., ‘New relations between G2 -geometries in dimensions 5 and 7’, Int. J. Math. 28(13) (2017), 1750094.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed