On the existence of G 2 class structures on a strictly nearly Kahler sixdimensional manifold | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2014. № 6 (32).

HomeIssuesOn the existence of G 2 class structures on a strictly nearly Kahler sixdimensional manifold | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2014. № 6 (32).

On the existence of G 2 class structures on a strictly nearly Kahler sixdimensional manifold

The strictly nearly Kahler 6-manifold (M, g, J, ю) is researched. Since the class G2 is the orthogonal complement to the class of nearly Kahler structures in the space of all classes of almost Hermitian structures, no strictly nearly Kahler structure can be simultaneously an almost Hermi-tian structure of the G 2 class. Can this class contain other structures, «close» to a strictly nearly Kahler structure, in the case of dimension six? There exist three families of almost Hermitian structures linked with the given structure (g, J, ю) on M, namely, H g, H J, and H w families of almost Hermitian structures with the same metric g, or the same almost complex structure J, or the same form ю, respectively. The problem whether a structure of the G 2 class can be present among structures belonging to those families is studied. It is proved that H and H J do not contain structures of the G 2 class. By an example of left-invariant structures on S xS = SU(2)xSU(2), it is proved that this is nevertheless possible for structures from H g.

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Keywords

strictly nearly Kahler manifolds, Gray - Hervella classification, строго приближенно кэлеровы многообразия, классификация Грэя - Хервеллы

Authors

NameOrganizationE-mail
Daurtseva Nataliya AlexandrovnaKemerovo State Universitynatali0112@ngs.ru
Всего: 1

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On the existence of G <sub>2</sub> class structures on a strictly nearly Kahler sixdimensional manifold | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2014. № 6 (32).

On the existence of G 2 class structures on a strictly nearly Kahler sixdimensional manifold | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2014. № 6 (32).