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Journal of Lie Theory 17 (2007), No. 3, 539--562
Copyright Heldermann Verlag 2007

Nearly Integrable SO(3) Structures on 5-Dimensional Lie Groups

Simon G. Chiossi
Institut fuer Mathematik, Humboldt-Universitaet, Unter den Linden 6, 10099 Berlin, Germany

Anna Fino
Dip. di Matematica, UniversitÓ di Torino, Via Carlo Alberto 10, 10123 Torino, Italy

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.

Keywords: SO(3) structure, connections with skewsymmetric torsion, symmetric space.

MSC: 53A40; 53C10, 53B15, 53C35, 53C25

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