Research Article
BibTex RIS Cite

On Semi-Tensor Bundle

Year 2018, Volume: 11 Issue: 1, 93 - 99, 30.04.2018

Furkan Yıldırım

https://doi.org/10.36890/iejg.545102
https://izlik.org/JA97MH74EK

Abstract

We investigate some lifts of tensor fields of type (1,0) on a cross-section in the semi-tensor (pullback)
bundle tM of tensor bundle TM of type (p,q) by using projection (submersion) of the
cotangent bundle T*M and we find some relation for them.

Keywords

Vector field complete lift cross-section horizontal lift pull-back bundle cotangent bundle semi-tensor bundle

References

  • [1] Isham, C.J., Modern Differential Geometry for Physicists. World Scientific, 1999.
  • [2] Fattaev, H., The lifts of vector fields to the semitensor bundle of the Type (2, 0). Journal of Qafqaz University, 25 (2009), no. 1, 136-140.
  • [3] Gezer, A., Salimov, A.A., Almost complex structures on the tensor bundles. Arab. J. Sci. Eng. Sect. A Sci., 33 (2008), no. 2, 283-296.
  • [4] Husemoller, D., Fibre Bundles. Springer, New York, 1994.
  • [5] Lawson, H.B. and Michelsohn, M.L., Spin Geometry. Princeton University Press., Princeton, 1989.
  • [6] Ledger, A.J. and Yano, K., Almost complex structure on tensor bundles. J. Dif. Geom., 1 (1967), 355-368.
  • [7] Salimov, A., Tensor Operators and their Applications. Nova Science Publ., New York, 2013.
  • [8] Salimov, A.A. and Kadıo˘ glu, E., Lifts of derivations to the semitangent bundle. Turk J. Math., 24 (2000), 259-266.
  • [9] Steenrod, N., The Topology of Fibre Bundles. Princeton University Press., Princeton, 1951.
  • [10] Yano, K. and Ishihara, S., Tangent and Cotangent Bundles. Marcel Dekker, Inc., New York, 1973.
  • [11] Yıldırım, F., On a special class of semi-cotangent bundle, Proceedings of the Institute of Mathematics and Mechanics, (ANAS) 41 (2015), no. 1, 25-38.
  • [12] Yıldırım, F. and Salimov A., Semi-cotangent bundle and problems of lifts. Turk J. Math., 38 (2014), 325-339.
  • [13] Yıldırım, F., Note on the cross-section in the semi-tensor bundle. New Trends in Mathematical Sciences, 5 (2017) , no. 2, 212-221.
  • [14] Yıldırım, F., Asl, M.B. and Jabrailzade, F., Vector and affinor fields on cross-sections in the semi-cotangent bundle. Proceedings of the Institute of Mathematics and Mechanics, (ANAS) 43 (2017), no. 2, 305-315.

Year 2018, Volume: 11 Issue: 1, 93 - 99, 30.04.2018

Furkan Yıldırım

https://doi.org/10.36890/iejg.545102
https://izlik.org/JA97MH74EK

Abstract

References

  • [1] Isham, C.J., Modern Differential Geometry for Physicists. World Scientific, 1999.
  • [2] Fattaev, H., The lifts of vector fields to the semitensor bundle of the Type (2, 0). Journal of Qafqaz University, 25 (2009), no. 1, 136-140.
  • [3] Gezer, A., Salimov, A.A., Almost complex structures on the tensor bundles. Arab. J. Sci. Eng. Sect. A Sci., 33 (2008), no. 2, 283-296.
  • [4] Husemoller, D., Fibre Bundles. Springer, New York, 1994.
  • [5] Lawson, H.B. and Michelsohn, M.L., Spin Geometry. Princeton University Press., Princeton, 1989.
  • [6] Ledger, A.J. and Yano, K., Almost complex structure on tensor bundles. J. Dif. Geom., 1 (1967), 355-368.
  • [7] Salimov, A., Tensor Operators and their Applications. Nova Science Publ., New York, 2013.
  • [8] Salimov, A.A. and Kadıo˘ glu, E., Lifts of derivations to the semitangent bundle. Turk J. Math., 24 (2000), 259-266.
  • [9] Steenrod, N., The Topology of Fibre Bundles. Princeton University Press., Princeton, 1951.
  • [10] Yano, K. and Ishihara, S., Tangent and Cotangent Bundles. Marcel Dekker, Inc., New York, 1973.
  • [11] Yıldırım, F., On a special class of semi-cotangent bundle, Proceedings of the Institute of Mathematics and Mechanics, (ANAS) 41 (2015), no. 1, 25-38.
  • [12] Yıldırım, F. and Salimov A., Semi-cotangent bundle and problems of lifts. Turk J. Math., 38 (2014), 325-339.
  • [13] Yıldırım, F., Note on the cross-section in the semi-tensor bundle. New Trends in Mathematical Sciences, 5 (2017) , no. 2, 212-221.
  • [14] Yıldırım, F., Asl, M.B. and Jabrailzade, F., Vector and affinor fields on cross-sections in the semi-cotangent bundle. Proceedings of the Institute of Mathematics and Mechanics, (ANAS) 43 (2017), no. 2, 305-315.
There are 14 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Furkan Yıldırım

Publication Date April 30, 2018
DOI https://doi.org/10.36890/iejg.545102
IZ https://izlik.org/JA97MH74EK
Published in Issue Year 2018 Volume: 11 Issue: 1

Cite

APA Yıldırım, F. (2018). On Semi-Tensor Bundle. International Electronic Journal of Geometry, 11(1), 93-99. https://doi.org/10.36890/iejg.545102
AMA 1.Yıldırım F. On Semi-Tensor Bundle. Int. Electron. J. Geom. 2018;11(1):93-99. doi:10.36890/iejg.545102
Chicago Yıldırım, Furkan. 2018. “On Semi-Tensor Bundle”. International Electronic Journal of Geometry 11 (1): 93-99. https://doi.org/10.36890/iejg.545102.
EndNote Yıldırım F (April 1, 2018) On Semi-Tensor Bundle. International Electronic Journal of Geometry 11 1 93–99.
IEEE [1]F. Yıldırım, “On Semi-Tensor Bundle”, Int. Electron. J. Geom., vol. 11, no. 1, pp. 93–99, Apr. 2018, doi: 10.36890/iejg.545102.
ISNAD Yıldırım, Furkan. “On Semi-Tensor Bundle”. International Electronic Journal of Geometry 11/1 (April 1, 2018): 93-99. https://doi.org/10.36890/iejg.545102.
JAMA 1.Yıldırım F. On Semi-Tensor Bundle. Int. Electron. J. Geom. 2018;11:93–99.
MLA Yıldırım, Furkan. “On Semi-Tensor Bundle”. International Electronic Journal of Geometry, vol. 11, no. 1, Apr. 2018, pp. 93-99, doi:10.36890/iejg.545102.
Vancouver 1.Furkan Yıldırım. On Semi-Tensor Bundle. Int. Electron. J. Geom. 2018 Apr. 1;11(1):93-9. doi:10.36890/iejg.545102

Cited By

Horizontal lift problems in a pull-back bundle of tensor bundles defined by projection of the cotangent bundles
Tbilisi Mathematical Journal
https://doi.org/10.32513/tmj/19322008143
On Pull-Back Bundle of Tensor Bundles Defined by Projection of The Cotangent Bundle
Applied Mathematics and Nonlinear Sciences
https://doi.org/10.2478/amns.2020.2.00066