Integrable G₂ Structures on 7-dimensional 3-Sasakian Manifolds

Year 2017, Volume: 21 Issue: 1, 254 - 260, 18.02.2017

Nülifer Özdemir , Şirin Akay

Abstract

It is known that there exist canonical and nearly parallel $G_2$ structures on 7-dimensional 3-Sasakian manifolds. In this paper, we investigate the existence of $G_2$ structures which are neither canonical nor nearly parallel. We obtain eight new $G_2$ structures on 7-dimensional 3-Sasakian manifolds which are of general type according to the classification of $G_2$ structures by Fernandez and Gray. Then by deforming the metric determined by the $G_2$ structure, we give integrable $G_2$ structures. On a manifold with integrable $G_2$ structure, there exists a uniquely determined metric covariant derivative with anti-symetric torsion. We write torsion tensors corresponding to metric covariant derivatives with skew-symmetric torsion. In addition, we investigate some properties of torsion tensors.

Keywords

G2 group, G2 structure; 3-Sasakian structure

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