Integrable G 2 Structures on 7-dimensional 3-Sasakian Manifolds

Authors : Nülifer ÖZDEMİR, Şirin AKAY

Pages : 254-260

Doi:10.19113/sdufbed.54977

View : 22 | Download : 11

Publication Date : 2017-02-18

Article Type : Research Paper

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