Complete lifts of vector fields to the special class of semi-tensor bundle

Yıl 2018, Cilt: 6 Sayı: 2, 332 - 337, 15.10.2018

Murat Polat

Öz

Using projection (submersion) of the cotangent bundle T*M over a manifold M, we define a semi-tensor (pull-back) bundle tM of type (p,q). The present paper is devoted to some results concerning with the complete lifts of vector fields from manifold M to its (p,q)-semitensor bundle.

Anahtar Kelimeler

complete lift, pull-back bundle, cotangent bundle, Vector Field

Kaynakça

• [1] A. Gezer, A. A. Salimov, Almost complex structures on the tensor bundles, Arab. J. Sci. Eng. Sect. A Sci. 33 (2008), no. 2, 283–296.
• [2] D. Husemolle, Fibre Bundles. Springer, New York, 1994.
• [3] H.B. Lawson and M.L. Michelsohn, Spin Geometry. Princeton University Press., Princeton, 1989.
• [4] A.J. Ledger and K. Yano, Almost complex structure on tensor bundles, J. Dif. Geom. 1 (1967), 355-368.
• [5] A. Salimov, Tensor Operators and their Applications. Nova Science Publ., New York, 2013.
• [6] A. A. Salimov and E. Kadıo˘glu, Lifts of Derivations to the Semitangent Bundle, Turk J. Math. 24 (2000), 259-266.
• [7] N. Steenrod, The Topology of Fibre Bundles. Princeton University Press., Princeton, 1951.
• [8] K. Yano and S. Ishihara, Tangent and Cotangent Bundles. Marcel Dekker, Inc., New York, 1973.
• [9] F. Yıldırım, A pull-back bundle of tensor bundles defined by projection of the tangent bundle,Ordu Univ. J. of Sci. and Tech., 7 (2017), no.2 ,353-366 .
• [10] F. Yıldırım, Diagonal lift in the semi-cotangent bundle and its applications.Turk J. Math.,42 (2018), no.3, 1312-1327.
• [11] F. Yıldırım, Note on the cross-section in the semi-tensor bundle, New Trends in Math. Sci., 5 (2017), no. 2, 212-221.
• [12] F. Yıldırım, On semi-tensor bundle, Int. Electron. J. Geom., 11 (2018), no.1, 93-99.
• [13] F. Yıldırım and A. Salimov, Semi-cotangent bundle and problems of lifts, Turk J. Math, (2014), 38, 325-339.
• [14] S. Yurttanc¸ıkmaz and F. Yıldırım, Musical isomorphisms on the semi-tensor bundles, Konuralp J. of Math, 6 (2018), no.1, 171-177.