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Note on the cross-section in the semi-tensor bundle

Year 2017, Volume: 5 Issue: 2, 212 - 221, 30.03.2017

Furkan Yildirim

Abstract

Using the fiber bundle M over a manifold B, we define a semi-tensor (pull-back) bundle tB of type (p,q). The complete and horizontal lift of projectable geometric objects on M to the semi-tensor (pull-back) bundle tB of type (p,q) are presented. The main purpose of this paper is to study the behaviour of complete lift of vector and affinor (tensor of type (1,1)) fields on cross-sections for pull-back (semi-tensor) bundle tB of type (p,q).

Keywords

Vector field complete lift horizontal lift pull-back bundle cross-section

References

  • T.V. Duc, Structure presque-transverse. J. Diff . Geom., 14(1979), No:2, 215-219.
  • C.J. Isham, ”Modern differential geometry for physicists”, World Scientific, 1999.
  • H. Fattaev, The Lifts of Vector Fields to the Semitensor Bundle of the Type (2, 0), Journal of Qafqaz University, 25 (2009), no. 1, 136-140.
  • A. Gezer and A. A. Salimov, Almost complex structures on the tensor bundles, Arab. J. Sci. Eng. Sect. A Sci. 33 (2008), no. 2, 283–296.
  • D. Husemoller, Fibre Bundles. Springer, New York, 1994.
  • V. Ivancevic and T. Ivancevic , Applied Differential Geometry, A Modern Introduction, World Scientific, Singapore, 2007.
  • H.B. Lawson and M.L. Michelsohn, Spin Geometry. Princeton University Press., Princeton, 1989.
  • A.J. Ledger and K. Yano, Almost complex structure on tensor bundles, J. Dif. Geom. 1 (1967), 355-368.
  • A. Salimov, Tensor Operators and their Applications. Nova Science Publ., New York, 2013.
  • A. A. Salimov and E. Kadıo˘glu, Lifts of derivations to the semitangent bundle, Turk J. Math. 24 (2000), 259-266.
  • N. Steenrod, The Topology of Fibre Bundles. Princeton University Press., Princeton, 1951.
  • V. V. Vishnevskii, Integrable affinor structures and their plural interpretations. Geometry, 7.J. Math. Sci. (New York) 108 (2002), no. 2, 151-187.
  • G. Walschap, Metric Structures in Differential Geometry, Graduate Texts in Mathematics, Springer-Verlag, New York, 2004.
  • F. Yıldırım, On a special class of semi-cotangent bundle, Proceedings of the Institute of Mathematics and Mechanics, (ANAS) 41 (2015), no. 1, 25-38.
  • F. Yıldırım and A. Salimov, Semi-cotangent bundle and problems of lifts, Turk J. Math, (2014), 38, 325-339.

Year 2017, Volume: 5 Issue: 2, 212 - 221, 30.03.2017

Furkan Yildirim

Abstract

References

  • T.V. Duc, Structure presque-transverse. J. Diff . Geom., 14(1979), No:2, 215-219.
  • C.J. Isham, ”Modern differential geometry for physicists”, World Scientific, 1999.
  • H. Fattaev, The Lifts of Vector Fields to the Semitensor Bundle of the Type (2, 0), Journal of Qafqaz University, 25 (2009), no. 1, 136-140.
  • A. Gezer and A. A. Salimov, Almost complex structures on the tensor bundles, Arab. J. Sci. Eng. Sect. A Sci. 33 (2008), no. 2, 283–296.
  • D. Husemoller, Fibre Bundles. Springer, New York, 1994.
  • V. Ivancevic and T. Ivancevic , Applied Differential Geometry, A Modern Introduction, World Scientific, Singapore, 2007.
  • H.B. Lawson and M.L. Michelsohn, Spin Geometry. Princeton University Press., Princeton, 1989.
  • A.J. Ledger and K. Yano, Almost complex structure on tensor bundles, J. Dif. Geom. 1 (1967), 355-368.
  • A. Salimov, Tensor Operators and their Applications. Nova Science Publ., New York, 2013.
  • A. A. Salimov and E. Kadıo˘glu, Lifts of derivations to the semitangent bundle, Turk J. Math. 24 (2000), 259-266.
  • N. Steenrod, The Topology of Fibre Bundles. Princeton University Press., Princeton, 1951.
  • V. V. Vishnevskii, Integrable affinor structures and their plural interpretations. Geometry, 7.J. Math. Sci. (New York) 108 (2002), no. 2, 151-187.
  • G. Walschap, Metric Structures in Differential Geometry, Graduate Texts in Mathematics, Springer-Verlag, New York, 2004.
  • F. Yıldırım, On a special class of semi-cotangent bundle, Proceedings of the Institute of Mathematics and Mechanics, (ANAS) 41 (2015), no. 1, 25-38.
  • F. Yıldırım and A. Salimov, Semi-cotangent bundle and problems of lifts, Turk J. Math, (2014), 38, 325-339.
There are 15 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Furkan Yildirim

Publication Date March 30, 2017
Published in Issue Year 2017 Volume: 5 Issue: 2

Cite

APA Yildirim, F. (2017). Note on the cross-section in the semi-tensor bundle. New Trends in Mathematical Sciences, 5(2), 212-221.
AMA Yildirim F. Note on the cross-section in the semi-tensor bundle. New Trends in Mathematical Sciences. March 2017;5(2):212-221.
Chicago Yildirim, Furkan. “Note on the Cross-Section in the Semi-Tensor Bundle”. New Trends in Mathematical Sciences 5, no. 2 (March 2017): 212-21.
EndNote Yildirim F (March 1, 2017) Note on the cross-section in the semi-tensor bundle. New Trends in Mathematical Sciences 5 2 212–221.
IEEE F. Yildirim, “Note on the cross-section in the semi-tensor bundle”, New Trends in Mathematical Sciences, vol. 5, no. 2, pp. 212–221, 2017.
ISNAD Yildirim, Furkan. “Note on the Cross-Section in the Semi-Tensor Bundle”. New Trends in Mathematical Sciences 5/2 (March 2017), 212-221.
JAMA Yildirim F. Note on the cross-section in the semi-tensor bundle. New Trends in Mathematical Sciences. 2017;5:212–221.
MLA Yildirim, Furkan. “Note on the Cross-Section in the Semi-Tensor Bundle”. New Trends in Mathematical Sciences, vol. 5, no. 2, 2017, pp. 212-21.
Vancouver Yildirim F. Note on the cross-section in the semi-tensor bundle. New Trends in Mathematical Sciences. 2017;5(2):212-21.
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