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

Nülifer Özdemir; Şirin Akay

doi:10.19113/sdufbed.54977

Integrable G2 Structures on 7-dimensional 3-Sasakian Manifolds

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

References

[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.

Details

Primary Language

Turkish

Subjects

-

Journal Section

-

Authors

Nülifer Özdemir

Şirin Akay This is me

Publication Date

February 18, 2017

Submission Date

October 14, 2016

Acceptance Date

-

Published in Issue

Year 2017 Volume: 21 Number: 1

DOI

https://doi.org/10.19113/sdufbed.54977

IZ

https://izlik.org/JA59BH46RK

Cite

RIS / Bibtex

APA

Özdemir, N., & Akay, Ş. (2017). Integrable G2 Structures on 7-dimensional 3-Sasakian Manifolds. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 21(1), 254-260. https://doi.org/10.19113/sdufbed.54977

AMA

1.Özdemir N, Akay Ş. Integrable G2 Structures on 7-dimensional 3-Sasakian Manifolds. J. Nat. Appl. Sci. 2017;21(1):254-260. doi:10.19113/sdufbed.54977

Chicago

Özdemir, Nülifer, and Şirin Akay. 2017. “Integrable G2 Structures on 7-Dimensional 3-Sasakian Manifolds”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21 (1): 254-60. https://doi.org/10.19113/sdufbed.54977.

EndNote

Özdemir N, Akay Ş (April 1, 2017) Integrable G2 Structures on 7-dimensional 3-Sasakian Manifolds. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21 1 254–260.

IEEE

[1]N. Özdemir and Ş. Akay, “Integrable G2 Structures on 7-dimensional 3-Sasakian Manifolds”, J. Nat. Appl. Sci., vol. 21, no. 1, pp. 254–260, Apr. 2017, doi: 10.19113/sdufbed.54977.

ISNAD

Özdemir, Nülifer - Akay, Şirin. “Integrable G2 Structures on 7-Dimensional 3-Sasakian Manifolds”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21/1 (April 1, 2017): 254-260. https://doi.org/10.19113/sdufbed.54977.

JAMA

1.Özdemir N, Akay Ş. Integrable G2 Structures on 7-dimensional 3-Sasakian Manifolds. J. Nat. Appl. Sci. 2017;21:254–260.

MLA

Özdemir, Nülifer, and Şirin Akay. “Integrable G2 Structures on 7-Dimensional 3-Sasakian Manifolds”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 21, no. 1, Apr. 2017, pp. 254-60, doi:10.19113/sdufbed.54977.

Vancouver

1.Nülifer Özdemir, Şirin Akay. Integrable G2 Structures on 7-dimensional 3-Sasakian Manifolds. J. Nat. Appl. Sci. 2017 Apr. 1;21(1):254-60. doi:10.19113/sdufbed.54977

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