Nearly integrable SO(3)-structures on 5-dimensional Lie groups

Details Nearly integrable SO(3)-structures on 5-dimensional Lie groups Nearly integrable SO(3)-structures on 5-dimensional Lie groups

2006-07-17

arxiv.org/abs/math/0607392v1

J. Lie Theory 17 (2007), no. 3, 539-562

Mathematics

Differential Geometry

22 pages

Scientific paper

Recent work Bobienski-Nurowski 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 under special behaviour of the onnection, which enables 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.

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