Geodesic
On approximately integrable $SO(3)$ structures on 5-dimensional manifolds
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2013), pp. 45-50

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In this work, irreducible $SO(3)$ structures on a 5-dimentional manifold are considered. The covariant divergence of the structure tensor is shown to be zero for approximately integrable irreducible $SO(3)$ structures. Examples of left invariant irreducible $SO(3)$ structures on 5-dimentional Lie groups that have a zero covariant divergence of the structure tensor but are not approximately integrable, as well as of irreducible $SO(3)$ structures with nonzero covariant divergence of the structure tensor are presented.
Keywords: special $SO(3)$ structure, 5-dimentional manifold
Mots-clés : Lie group. 
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     author = {A. G. Sedykh},
     title = {On approximately integrable $SO(3)$ structures on 5-dimensional manifolds},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {45--50},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2013_3_a5/}
}
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A. G. Sedykh. On approximately integrable $SO(3)$ structures on 5-dimensional manifolds. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2013), pp. 45-50. http://geodesic.mathdoc.fr/item/VTGU_2013_3_a5/