Some Notes On (2,0)-Semitensor Bundle

Abstract

We investigate some lifts of vector fields on a cross-section in the semi-tensor (pull-back) bundle tM of tensor bundle of type (2,0) by using projection (submersion) of the tangent bundle TM and we find some relation for them.

Keywords

• Cross-section,pull-back bundle,tangent bundle,semi-tensor bundle

References

1. [1] Isham C.J., ”Modern Differential Geometry for Physicists”, World Scientific, 1999.
2. [2] Fattaev H., Tensor fields on cross-section in the tensor bundle of the type (2,0). News of Baku Univ., Physico-mathematical Sciences Series, (2008), no: 4, p.35-43.
3. [3] 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.
4. [4] 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.
5. [5] Husemoller D. Fibre Bundles. Springer, New York, 1994.
6. [6] Lawson H.B. And Michelsohn M.L. Spin Geometry. Princeton University Press., Princeton, 1989.
7. [7] Ledger A.J. and Yano K. Almost complex structure on tensor bundles, J. Dif. Geom. 1 (1967), 355-368.
8. [8] Pontryagin L.S. Characteristic cycles on differentiable manifolds. Amer. Math. Soc. Translation, 1950 (1950), no. 32, 72 pp.

9. [9] Salimov A. Tensor Operators and their Applications. Nova Science Publ., New York, 2013.
10. [10] Salimov A.A. and Kadıo˘glu E. Lifts of derivations to the semitangent Bundle, Turk J. Math., (2000) 24, 259-266.
11. [11] Salimov A., Gezer A. and Akbulut K. Geodesics of Sasakian metrics on tensor bundles, Mediterr. J. Math. 2, 135-147
12. [12] Steenrod N. The Topology of Fibre Bundles. Princeton University Press., Princeton, 1951.
13. [13] Yano K. And Ishihara S. Tangent and Cotangent Bundles. Marcel Dekker, Inc., New York, 1973.
14. [14] 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.
15. [15] Yıldırım F. and Salimov A. Semi-cotangent bundle and problems of lifts, Turk J. Math, (2014), 38, 325-339.