On conformal change of projective Ricci curvature of Kropina metrics

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran. b.rezaei@urmia.ac.ir

2 Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran. s.jalili@urmia.ac.ir

3 Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran. l.ghasemnezhad@urmia.ac.ir

Abstract

In this paper‎, ‎we study and investigate the conformal change of projective Ricci curvature of Kropina metrics‎. ‎Let F and  F˜ be two conformally related Kropina metrics on a manifold M‎. ‎We prove that PRic˜=  PRic if and only if the conformal transformation is a homothety‎.

Keywords

References

  • 1. S. B´acs´o and X. Cheng, Finsler conformal transformations and the curvature invariances, Publ. Math. Debrecen, 70(2007), 221-231.
  • 2. X. Cheng, Y. Shen, and X. Ma, On a class of projective Ricci flat Finsler metrics,
    Publ. Math. Debrecen. 7528(2017), 1-12.
  • 3. X. Cheng and Z. Shen, Finsler Geometry: An Approach via Randers Spaces,
    Springer, 2012.
  • 4. K. Kaur and G. Shanker, On the geodesics of a homogeneous Finsler space with a
    special (α, β)-metric, Journal of Finsler Geometry and its Applications, 1(1) (2020),
    26-36.
  • 5. X. Cheng, X. Ma and Y.Shen , On Projective Ricci Flat Kropina Metrics, Journal
    of Mathematics, 37(4) (2017), 705-713.
  • 6. L. Ghasemnezhad, B.Rezaei and M.Gabreni, On isotropic projective Ricci curvature
    of C-reducible Finsler metrics, Turkish Journal of Mathematics, 43(3) (2019), 1730-
    1741.
  • 7. V. K. Kropina, On projective two-dimensional Finsler spaces with a special metric,
    Trudy Sem. Vektor. Tenzor. Anal. 11(1961), 277-292.
  • 8. V.K. Matsumoto, On projective two-dimensional Finsler spaces with a special metric,
    Trudy Sem. Vektor. Tenzor. Anal., 11(1961), 277-292.
  • 9. H. Sadeghi, A special class of Finsler metrics, Journal of Finsler Geometry and its
    Applications, 1(1) (2020), 60-65.
  • 10. Z. Shen, Volume comparison and applications in Riemann-Finsler geometry, Advances in Math. 128 (1997), 306-328.
  • 11. Z. Shen, Differential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, 2001.
  • 12. A. Tayebi and T. Tabatabaeifar, Matsumoto metrics of reversible curvature, Acta
    Mathematica Academiae Paedagogicae Nyiregyhaziensis., 32(2016), 165-200.
  • 13. X. Zhang and Y. Shen, On Einstein Matsumoto metrics, arXiv:math/1207.1944v1
    [math.DG] 9 Jul 2012
Journal of Finsler Geometry and its Applications
Volume 2, Issue 2
December 2021
Pages 1-13

Files

Share

How to cite

Statistics