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Musical Isomorphisms on the Semi-Tensor Bundles

Year 2018, Volume: 6 Issue: 1, 171 - 177, 15.04.2018

Semra Yurttançıkmaz Furkan Yıldırım

Abstract

We transfer vertical lifts and complete lifts of some tensor fields from the semi-tangent bundle $tM$ to the semi-cotangent bundle $t^{\ast }M$ \ using a musical isomorphism between these bundles. In this article, we also analyze complete lift of vector and affinor (tensor of type $(1,1)$) fields for semi-tangent (pull-back) bundle $tM$. Finally, we study compatibility of transferring lifts with complete lifts in the semi-cotangent bundle $t^{\ast }M$.

Keywords

Semi-tensor bundle complete lift musical isomorphism vector field pull-back bundle

References

  • [1] A. A. Salimov, E. Kadioglu Lifts of derivations to the semitangent bundle. Turk J Math 2000; 24: 259-266.
  • [2] D. Husem¨oller, Fibre Bundles. New York, NY, USA: Springer, 1994.
  • [3] F. Yildirim, On a special class of semi-cotangent bundle, Proceedings of the Institute of Mathematics and Mechanics, (ANAS) 41 (2015), no. 1, 25-38.
  • [4] F. Yildirim and A. Salimov, Semi-cotangent bundle and problems of lifts, Turk J. Math, (2014), 38, 325-339.
  • [5] H.B. Lawson and M.L. Michelsohn, Spin Geometry, Princeton University Press., Princeton, 1989.
  • [6] K. Yano and S. Ishihara, Tangent and Cotangent Bundles , Marcel Dekker, Inc., New York, 1973.
  • [7] N. Steenrod, The Topology of Fibre Bundles. Princeton University Press., Princeton, 1951.
  • [8] R. Cakan, K. Akbulut, A. Salimov, Musical isomorphisms and problems of lifts, Chin. Ann. Math. Ser. B. (2016) 37: 323.
  • [9] T.V. Duc, Structure presque-transverse. J. Diff. Geom., 14(1979), No:2, 215-219.
  • [10] V. V. Vishnevskii, Integrable affinor structures and their plural interpretations, Geometry, 7.J. Math. Sci., (New York) 108 (2002), no. 2, 151-187.
  • [11] V. Vishnevskii, A.P. Shirokov and V.V. Shurygin, Spaces over Algebras. Kazan. Kazan Gos. Univ. 1985 (in Russian).

Year 2018, Volume: 6 Issue: 1, 171 - 177, 15.04.2018

Semra Yurttançıkmaz Furkan Yıldırım

Abstract

References

  • [1] A. A. Salimov, E. Kadioglu Lifts of derivations to the semitangent bundle. Turk J Math 2000; 24: 259-266.
  • [2] D. Husem¨oller, Fibre Bundles. New York, NY, USA: Springer, 1994.
  • [3] F. Yildirim, On a special class of semi-cotangent bundle, Proceedings of the Institute of Mathematics and Mechanics, (ANAS) 41 (2015), no. 1, 25-38.
  • [4] F. Yildirim and A. Salimov, Semi-cotangent bundle and problems of lifts, Turk J. Math, (2014), 38, 325-339.
  • [5] H.B. Lawson and M.L. Michelsohn, Spin Geometry, Princeton University Press., Princeton, 1989.
  • [6] K. Yano and S. Ishihara, Tangent and Cotangent Bundles , Marcel Dekker, Inc., New York, 1973.
  • [7] N. Steenrod, The Topology of Fibre Bundles. Princeton University Press., Princeton, 1951.
  • [8] R. Cakan, K. Akbulut, A. Salimov, Musical isomorphisms and problems of lifts, Chin. Ann. Math. Ser. B. (2016) 37: 323.
  • [9] T.V. Duc, Structure presque-transverse. J. Diff. Geom., 14(1979), No:2, 215-219.
  • [10] V. V. Vishnevskii, Integrable affinor structures and their plural interpretations, Geometry, 7.J. Math. Sci., (New York) 108 (2002), no. 2, 151-187.
  • [11] V. Vishnevskii, A.P. Shirokov and V.V. Shurygin, Spaces over Algebras. Kazan. Kazan Gos. Univ. 1985 (in Russian).
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Semra Yurttançıkmaz

Furkan Yıldırım

Publication Date April 15, 2018
Submission Date July 2, 2017
Acceptance Date April 6, 2018
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

APA Yurttançıkmaz, S., & Yıldırım, F. (2018). Musical Isomorphisms on the Semi-Tensor Bundles. Konuralp Journal of Mathematics, 6(1), 171-177.
AMA Yurttançıkmaz S, Yıldırım F. Musical Isomorphisms on the Semi-Tensor Bundles. Konuralp J. Math. April 2018;6(1):171-177.
Chicago Yurttançıkmaz, Semra, and Furkan Yıldırım. “Musical Isomorphisms on the Semi-Tensor Bundles”. Konuralp Journal of Mathematics 6, no. 1 (April 2018): 171-77.
EndNote Yurttançıkmaz S, Yıldırım F (April 1, 2018) Musical Isomorphisms on the Semi-Tensor Bundles. Konuralp Journal of Mathematics 6 1 171–177.
IEEE S. Yurttançıkmaz and F. Yıldırım, “Musical Isomorphisms on the Semi-Tensor Bundles”, Konuralp J. Math., vol. 6, no. 1, pp. 171–177, 2018.
ISNAD Yurttançıkmaz, Semra - Yıldırım, Furkan. “Musical Isomorphisms on the Semi-Tensor Bundles”. Konuralp Journal of Mathematics 6/1 (April 2018), 171-177.
JAMA Yurttançıkmaz S, Yıldırım F. Musical Isomorphisms on the Semi-Tensor Bundles. Konuralp J. Math. 2018;6:171–177.
MLA Yurttançıkmaz, Semra and Furkan Yıldırım. “Musical Isomorphisms on the Semi-Tensor Bundles”. Konuralp Journal of Mathematics, vol. 6, no. 1, 2018, pp. 171-7.
Vancouver Yurttançıkmaz S, Yıldırım F. Musical Isomorphisms on the Semi-Tensor Bundles. Konuralp J. Math. 2018;6(1):171-7.
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