- Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Vol: 21 Issue: 1
- Integrable G 2 Structures on 7-dimensional 3-Sasakian Manifolds
Integrable G 2 Structures on 7-dimensional 3-Sasakian Manifolds
Authors : Nülifer Özdemir, Şirin Akay
Pages : 254-260
Doi:10.19113/sdufbed.54977
View : 10 | Download : 5
Publication Date : 2017-04-15
Article Type : Other
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