Journal of Lie Theory

no. 3
Nearly Integrable SO(3) Structures on 5-Dimensional Lie Groups
Simon G. Chiossi1; Anna Fino2
1Institut fuer Mathematik, Humboldt-Universitaet, Unter den Linden 6, 10099 Berlin, Germany
2Dip. di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 539-562
Recent work of M. Bobienski and P. Nurowski [J. Reine Angew. Math., to appear] on 5-dimensional Riemannian manifolds with an SO(3) structure prompts us to investigate which Lie groups admit such a geometry. The case in which the SO(3) structure admits a compatible connection with torsion is considered. This leads to a classification with respect to special behaviour of the connection, which enables us to recover all known examples, plus others bearing torsion of pure type. Suggestive relations with special structures in other dimensions are highlighted, with attention to eight-dimensional SU(3) geometry.
DOI: 10.5802/jolt.460
Classification: 53A40, 53C10, 53B15, 53C35, 53C25
Keywords: SO(3) structure, connections with skewsymmetric torsion, symmetric space

Simon G. Chiossi  1 ; Anna Fino  2

1 Institut fuer Mathematik, Humboldt-Universitaet, Unter den Linden 6, 10099 Berlin, Germany
2 Dip. di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy 
Simon G. Chiossi; Anna Fino. Nearly Integrable SO(3) Structures on 5-Dimensional Lie Groups. Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 539-562. doi: 10.5802/jolt.460
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