SavedAdd your journal

Journals / Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 21 Sayı: 1

Integrable G<sub>2</sub> Structures on 7-dimensional 3-Sasakian Manifolds

Nülifer Özdemir
Şirin Akay
Pages
254–260
Publication Date
2017-02-18
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In addition, we investigate some properties of torsion tensors.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:It is known that there exist canonical and nearly parallel $G_2$ structures on 7-dimensional 3-Sasakian manifolds.
📊
Key Findings & Data:In this paper, we investigate the existence of $G_2$ structures which are neither canonical nor nearly parallel.
💡
Conclusion & Impact:In addition, we investigate some properties of torsion tensors.
🔬Design:Makale
📍Scope:Comprehensive Sample
⚙️Variables:G2 group · G2 structure · 3-Sasakian structure

Özet

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.

🔖

Cite This Article

Özdemir, N. (2017). Integrable G<sub>2</sub> Structures on 7-dimensional 3-Sasakian Manifolds. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 21 Sayı: 1, 254–260. https://doi.org/10.19113/sdufbed.54977

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (8)

  1. Bryant, R. L., Metrics with Exceptional Holonomy, Ann. of Math., 126 (1987), 525-586.
  2. Fernández, M. and Gray, A., Riemannian Manifolds with Structure Group G2, Ann. Mat. Pura Appl. (4) 132 (1982) 19-25.
  3. Cabrera, F. M., On Riemannian Manifolds with G2- Structure, Bolletino U.M.I (7) 10-A (1996) 99-112.
  4. Boyer, C.P and Galicki, K., 3-Sasakian Manifolds, Surveys Diff. Geom., 7, (1999) 123-184, arXiv:hep-th/ 9810250.
  5. Agricola, I. and Friedrich, T., 3-Sasakian Manifolds in Dimension Seven, Their Spinors and G2 Structures, Journal of Geometry and Physics 60 (2010) 326-332.
  6. Friedrich,T.,Kath,I.,Moroianu,A.andSemmelmann, U., On Nearly Parallel G2 Structures, J. Geom. Phys., 23 (1997) 256-286.
  7. Friedrich, T. and Ivanov, S., Parallel Spinors and Con- nections with Skew-Symmetric Torsion in String The- ory, Asian Jour. Math., 6 (2002) 303-336.
  8. Agricola, I., The Srni Lectures on Non-Integrable Ge- ometries with Torsion, Math. Ann., 328 (2004) 711- 748.