On approximately integrable SO(3) structures on 5-dimensional manifolds | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2013. № 3(23).

On approximately integrable SO(3) structures on 5-dimensional manifolds

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.

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Keywords

специальная SO(3)-структура, пятимерное многообразие, группа Ли, special SO(3) structure, 5-dimentional manifold, Lie group

Authors

Name	Organization	E-mail
Sedykh Anna Gennad'evna	Kemerovo State University	Nuska2522@mail.ru

Всего: 1

References

Bobienski M.M., Nurowski P. Irreducible SO(3) geometry in dimension five. arXiv:math/ 0507152v3 [math.DG], 2005.

Fino A.A., Chiossi S.G. Nearly integrable SO(3) structures on 5-dimentional lie groups // J. Lie Theory. 2007. V. 17. No. 3. P. 539-562. (arXiv:math/0607392v1 [math.DG]).

Diatta A. Left invariant contact structures on Lie groups // arXiv:math/0403555v2 [math.DG], 2004.

Кобаяси Ш.,Намидзу К. Основы дифференциальной геометрии: в 2 т. М.: Наука, 1981.

Agricola I. The Srni lectures on non-integrable geometries with torsion // arXiv:math/ 0606705v1