Skip to main content
SpringerLink
Log in

Tensor Fields of Type (0, 2) on the Tangent Bundle of a Riemannian Manifold

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

To any (0, 2)-tensor field on the tangent bundle of a Riemannian manifold, we associate a global matrix function. Based on this fact, natural tensor fields are defined and characterized, essentially by means of well-known algebraic results. In the symmetric case, this classification coincides with the one given by Kowalski–Sekizawa; in the skew-symmetric one, it does with that obtained by Janyška.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Gromoll, D., Klingenberg, W. and Meyer, W.: Riemannsche Geometrie im Großen, Lecture Notes in Math. 55, Springer, New York, 1968.

    Google Scholar 

  2. Janyška, J.: Natural 2-forms on the tangent bundle of a Riemannian manifold, Rend. Cir. Mat. Palermo (2). Suppl. 32 (1994), 165–174.

    Google Scholar 

  3. Kolář, I., Michor, P. and Slovák, J.: Natural Operations in Differential Geometry, Springer-Verlag, New York, 1993.

    Google Scholar 

  4. Kowalski, O. and Sekizawa, M.: Natural transformations of Riemannian metrics on manifolds to metrics on tangent bundles – a classification, Bull. Tokyo Gakugei Univ. (4), 40 (1988), 1–29.

    Google Scholar 

  5. Krupka, D.: Elementary theory of differential invariants, Arch. Math. (Brno) 4 (1978), 207–214.

    Google Scholar 

  6. Krupka, D.: Differential invariants, Lecture Notes, Faculty of Science, Purkyně University, Brno, 1979.

    Google Scholar 

  7. Krupka, D. and Janyška, J.: Lectures on Differential Invariants, Folia Fac. Sci. Nat. Univ. Purkynianae Brunensis, Brno, 1990.

    Google Scholar 

  8. Krupka, D. and Mikolášová, V.: On the uniqueness of some differential invariants: d, [,], ▽, Czechoslovak Math. J. 34 (1984), 588–597.

    Google Scholar 

  9. Musso, E. and Tricerri, F.: Riemannian metrics on tangent bundles, Ann. Mat. Pura Appl. (4), 150 (1988), 1–19.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, (1428), Buenos Aires, Argentina

    Maria del Carmen Calvo & Guillermo G. R. Keilhauer

Authors
  1. Maria del Carmen Calvo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guillermo G. R. Keilhauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Calvo, M.d.C., Keilhauer, G.G.R. Tensor Fields of Type (0, 2) on the Tangent Bundle of a Riemannian Manifold. Geometriae Dedicata 71, 209–219 (1998). https://doi.org/10.1023/A:1005084210109

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1005084210109

Search

Navigation