Conformal gradient fields on Finsler manifolds


In this note, some basic structural conditions that are imposed on a Finsler manifold as a consequence of existence of a conformal gradient field are presented. Then, after reiterating the definition of warped product Finsler manifolds and the constituents of its related variational problem, the correlation between geodesics of this warped product structure and geodesics of its constructing Finsler manifolds is studied.

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


  1. 1.

    H. Akbar-Zadeh, Transformations infinitésimales conformes des variétés finsleriennes compactes. Ann. Polon. Math. XXXVI, 213–229 (1979)

    MathSciNet  Article  Google Scholar 

  2. 2.

    G.S. Asanov, Finslerian metric functions over the product \(R \times M\) and their potential applications. Rep. Math. Phys. 41, 117–132 (1998)

    MathSciNet  Article  Google Scholar 

  3. 3.

    D. Bao, S.S. Chern, Z. Shen, Riemann–Finsler geometry (Springer, Berlin, 2000)

    Google Scholar 

  4. 4.

    B. Bidabad, P. Joharinad, Conformal vector fields on complete Finsler spaces of constant Ricci curvature. J. Differ. Geom. Appl. 33, 75–84 (2014)

    MathSciNet  Article  Google Scholar 

  5. 5.

    H.W. Brinkmann, Einstein spaces which are mapped conformally on each other. Math. Ann. 94, 119–145 (1925)

    MathSciNet  Article  Google Scholar 

  6. 6.

    P. Joharinad, Warped product Finsler manifolds from Hamiltonian point of view. Int. J. Geom. Methods Mod. Phys. 14(2), 1750029-1–1750029-16 (2017)

    MathSciNet  Article  Google Scholar 

  7. 7.

    P. Joharinad, B. Bidabad, Conformal vector fields on Finsler spaces. J. Differ. Geom. Appl. 31, 33–40 (2013)

    MathSciNet  Article  Google Scholar 

  8. 8.

    L. Kozma, I.R. Peter, V. Varga, Warped product of Finsler manifolds. Ann. Univ. Sci. Bp. Eotvos Sect. Math. 44, 157–170 (2001)

    MathSciNet  MATH  Google Scholar 

  9. 9.

    Z. Shen, Lectures on Finsler Geometry (World Scientific Pub Co Inc, Singapore, 2001)

    Google Scholar 

  10. 10.

    Z. Shen, Differential Geometry of Spray and Finsler Spaces (Kluwer, Dordrecht, 2001)

    Google Scholar 

  11. 11.

    Y. Tashiro, Complete Riemannian manifolds and some vector fields. Trans. AMS 117, 251–275 (1965)

    MathSciNet  Article  Google Scholar 

  12. 12.

    K. Yano, The Theory of Lie Derivatives and Its Applications (North Holland, Amsterdam, 1957)

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Parvaneh Joharinad.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Joharinad, P. Conformal gradient fields on Finsler manifolds. Period Math Hung 82, 87–97 (2021).

Download citation


  • Finsler manifolds
  • Conformal gradient fields
  • Warped product

Mathematics Subject Classification

  • 53A30
  • 30C35
  • 58B20