On H-curvature of Finsler warped product metrics

Document Type : Original Article

Authors

1 Department of mathematics, Istanbul Bilgi University, Istanbul, Turkey. E-mail: esra.sengelen@bilgi.edu.tr

2 Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran. E-mail: m.gabrani@urmia.ac.ir

Abstract

In this paper, we study the H-curvature, an important non-Riemannian quantity, for a rich and important class of Finsler metrics called Finsler warped product metrics. We find an equation that characterizes the metrics of almost vanishing H-curvature. Further, we show that, if F is a Finsler warped product metric, then the H-curvature vanishes if and only if the Χ-curvature vanishes.






Keywords

References

  • 1. H. Akbar-Zadeh, Sur les espaces de Finsler a` courbures sectionnelles constantes. Acad.
    Roy. Belg. Bull. Cl. Sci. 74(5)(1988), 281-322.
  • 2. S.S. Chern and Z. Shen, Riemann-Finsler Geometry, World Scientic Publishers, 2004.
  • 3. B. Chen, Z. Shen and L. Zhao, Constructions of Einstein Finsler metrics by warped
    product, preprint, (2016).
  • 4. L. Huaifu, M. Xiaohuan and Z. Hongzhen, Finsler warped product metrics with special
    Riemannian curvature properties. Science China Math.
  • 5. B. Li and Z. Shen, On some non-Riemannian quantities in Finsler Geometry. Canad.
    Math. Bull. 56(2013), 184-293.
  • 6. H. Liu, X. Mo and H. Zhang, Finsler warped product metrics with special Riemannian
    curvature properties, Science China Mathematics. 2019; 1-18.
  • 7. H. Liu and X. Mo, Finsler warped product metrics of Douglas type. Canadian Mathematical Bulletin, https://cms.math.ca/10.4153/CMB-2017-077-0.
  • 8. X. Mo, On the non-Riemannian quantity H of a Finsler metric, Differ. Geom. Appl.
    27(1)(2009), 7-14.
  • 9. X. Mo, A class of Finsler metrics with almost vanishing H-curvature, Balkan. J. Geom.
    Appl. 21(2016), 58-66.
  • 10. P. J. McCarthy and S. F. Rutz, The general general four-dimensional spherically symmetric Finsler space, Gen. Relativity Gravitation. 25(1993), 589-602.
  • 11. B. Najafi, Z. Shen and A. Tayebi, Finsler metrics of scalar flag curvature with special
    non-Riemannian curvature properties, Geometriae Dedicata. 131(2008), 87-97.
  • 12. B. Najafi, B. Bidabad and A. Tayebi, On R-quadratic Finsler metrics, Iran. J. Sci.
    Tech. Tran. A. Science. 31(2007), 439-443.
  • 13. S. Rutz, Symmetry in Finsler spaces, Finsler geometry. Contemp. Math. 196(1996),
    289-300.
  • 14. E. S. Sevim, Z. Shen and S. Ulgen, Spherically symmetric Finsler metrics with constant
    Ricci and flag curvature, 2015.
  • 15. Z. Shen, On some non-Riemannian quantities in Finsler geometry, Canad. Math. Bull.
    56(2013), 184-193.
  • 16. Z. Shen, Volume comparison and its applications in Riemannian-Finsler geometry, Advances in Math. 128(1997), 306-328.
  • 17. D. Tang, On the non-Riemannian quantity H in Finsler geometry, Differ. Geom. Appl.
    29(2011), 207-213.
  • 18. A. Tayebi and M. Razgordani, On H-curvature of (α, β)-metrics, Turkish J. Math.
    44(2020), 207-222.
  • 19. A. Tayebi and H. Sadeghi, Generalized P-reducible (α, β)-metrics with vanishing Scurvature, Ann. Polon. Math. 114(2015), 67-79.
Journal of Finsler Geometry and its Applications
Volume 1, Issue 1
July 2020
Pages 37-44

Files

Share

How to cite

Statistics