Some rigidity results on homogeneous Finsler spaces equipped with Killing frames

Document Type : Original Article

Authors

1 Department of Mathematics, Bijar Branch, Islamic Azad University, Bijar, Iran

2 Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran

Abstract

Utilizing Killing frames on homogeneous Finsler manifolds, we express the Berwald and mean Berwald curvatures in terms of Killing frames and get some rigidity results among them we prove that homogeneous isotropic weakly Berwald metrics reduce to weakly Berwald metric.

Keywords

References

  • 1. R. Gangopadhyay, A. Shriwastawa and B. Tiwari, On Finsler warped product metrics
    with vanishing E-curvature, AUT J. Math. Computing, 2(2021), 137-142.
  • 2. P. Habibi, Homogeneous geodesics in homogeneous Randers spaces - examples, J. Finsler
    Geom. Appl., 1(1) (2020), 89-95.
  • 3. L. Huang, On the fundamental equations of homogeneous Finsler spaces, Differ. Geom.
    Appl. 40(2015), 187-208.
  • 4. Z. Hu and S. Deng, Killing fields and curvatures of homogeneous Finsler manifolds,
    Publ. Math. Debrecen, 94(2019), 215-229.
  • 5. E. S. Sevim; M. Gabrani, On Finsler metrics with weakly isotropic S-curvature, AUT J.
    Math. Computing, 2(2021), 143-151.
  • 6. Z. Shen, Volume comparison and its applications in Riemann-Finsler geometry, Adv.
    Math. 128(1997) 306-328.
  • 7. A. Tayebi and B. Najafi, On a class of homogeneous Finsler metrics, J. Geom. Phys.
    140(2019), 265-270.
  • 8. A. Tayebi and E. Peyghan, On Douglas surfaces, Bull. Math. Soc. Science. Math.
    Roumanie, Tome 55 (103), No 3, (2012), 327-335.
  • 9. A. Tayebi and M. Rafie. Rad, S-curvature of isotropic Berwald metrics, Sci. China. Series
    A: Math. 51(2008), 2198-2204.
  • 10. A. Tayebi and M. Razgordani, On H-curvature of (α, β)-metrics, Turkish. J. Math.
    44(2020), 207-222.
  • 11. A. Tayebi and H. Sadeghi, On generalized Douglas-Weyl (α, β)-metrics, Acta Mathematica Sinica, English Series. 31(10) (2015), 1611-1620.
  • 12. A. Tayebi and T. Tabatabeifar, Unicorn metrics with almost vanishing H- and Ξcurvatures, Turkish. J. Math. 41(2017), 998-1008.
  • 13. Q. Xia, Some results on the non-Riemannian quantity H of a Finsler metric, Int. J.
    Math. 22(2011), 925-936.
  • 14. M. Xu and S. Deng, Killing frames and S-curvature of homogeneous Finsler spaces,
    Glasgow Mathematical Journal, 57(2015), 457-464.
  • 15. M. Xu, S. Deng, L. Huang and Z. Hu, Even-dimensional homogeneous Finsler spaces
    with positive flag curvature, Indiana Univ. Math. J. 66(2017), 949-972.
  • 16. M. Zeinali Laki, Flag curvature of invariant 3-power metrics on homogeneous spaces, J.
    Finsler Geom. Appl., 4(1) (2023), 124-132. 
Journal of Finsler Geometry and its Applications
Volume 5, Issue 1
2024
Pages 135-143

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