Öz
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.
Anahtar Kelimeler
Kaynakça
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Ayrıntılar
| Bölüm | Makaleler |
|---|---|
| Yazarlar | |
| Yayımlanma Tarihi | 18 Şubat 2017 |
| Yayımlandığı Sayı | Yıl 2017 Cilt: 21 Sayı: 1 |
