Geodesic
Nearly Integrable SO(3) Structures on 5-Dimensional Lie Groups
Journal of Lie theory, Tome 17 (2007) no. 3, pp. 539-562

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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.
Classification : 53A40, 53C10, 53B15, 53C35, 53C25
Mots-clés : SO(3) structure, connections with skewsymmetric torsion, symmetric space 
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     author = {S. G. Chiossi and A. Fino },
     title = {Nearly {Integrable} {SO(3)} {Structures} on {5-Dimensional} {Lie} {Groups}},
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S. G. Chiossi; A. Fino . Nearly Integrable SO(3) Structures on 5-Dimensional Lie Groups. Journal of Lie theory, Tome 17 (2007) no. 3, pp. 539-562. http://geodesic.mathdoc.fr/item/JLT_2007_17_3_JLT_2007_17_3_a5/