Skip to main content

Musical isomorphisms and problems of lifts

Chinese Annals of Mathematics, Series B volume 37, pages 323–330 (2016)Cite this article

Abstract

Using the complete lift on tangent bundles, the authors construct the complete lift on cotangent bundles of tensor fields with the aid of a musical isomorphism. In this new framework, the authors have a new intrepretation of the complete lift of tensor fields on cotangent bundles.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. Bejan, C., Almost para-Hermitian structures on the tangent bundle of an almost para-co-Hermitian manifold, Proceedings of the Fifth National Seminar of Finsler and Lagrange Spaces (Brasov, 1988), Soc. Stiinte Mat. R. S., Romania, Bucharest, 1989, 105–109.

    Google Scholar 

  2. Cruceanu, V., Une classe de structures géométriques sur le fibré cotangent, International Conference on Differential Geometry and Its Applications (Bucharest, 1992), Tensor (N. S.), Vol. 53, Commemoration Volume I, 1993, 196–201.

    Google Scholar 

  3. Cruceanu, V., Fortuny, P. and Gadea, P. M., A survey on paracomplex geometry, Rocky Mountain J. Math., 26(1), 1996, 83–115.

    Article  MathSciNet  MATH  Google Scholar 

  4. Druta, S. L., Classes of general natural almost anti-Hermitian structures on the cotangent bundles, Mediterr. J. Math., 8(2), 2011, 161–179.

    Article  MathSciNet  MATH  Google Scholar 

  5. Druta-Romaniuc, S. L., Riemannian almost product and para-Hermitian cotangent bundles of general natural lift type, Acta Math. Hungar., 139(3), 2013, 228–244.

    Article  MathSciNet  MATH  Google Scholar 

  6. Salimov, A. A., On operators associated with tensor fields, J. Geom., 99(1–2), 2010, 107–145.

    Article  MathSciNet  MATH  Google Scholar 

  7. Yano, K. and Ako, M., On certain operators associated with tensor fields, Kodai Math. Sem. Rep., 20, 1968, 414–436.

    Article  MathSciNet  MATH  Google Scholar 

  8. Yano, K. and Ishihara, S., Tangent and cotangent bundles, Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 1973.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Ataturk University, Erzurum, 25240, Turkey

    Rabia Cakan, Kursat Akbulut & Arif Salimov

  2. Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Az1001, 30, Istiglaliyyat str., Baku, Azerbaijan Republic

    Arif Salimov

Authors
  1. Rabia Cakan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kursat Akbulut
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arif Salimov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rabia Cakan.

Additional information

This work was supported by the Scientific and Technological Research Council of Turkey (No. 112T111).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Cakan, R., Akbulut, K. & Salimov, A. Musical isomorphisms and problems of lifts. Chin. Ann. Math. Ser. B 37, 323–330 (2016). https://doi.org/10.1007/s11401-016-0980-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11401-016-0980-6

Keywords

  • Tensor fields
  • Cotangent bundles
  • Complete lift
  • Anti-Hermitian metric
  • Riemannian extension

2000 MR Subject Classification

  • 53A45
  • 55R10
  • 53C56