On projective Riemann quadratic (PR-quadratic) Finsler metrics

Document Type : Original Article

Author

Department of Mathematics, Faculty of Science, University of Qom, Qom. Iran

Abstract

This paper focuses on Projective Riemann quadratic (PR-quadratic) Finsler metrics, which are a variant of the Finsler metric in Finsler geometry. The paper introduces a special class of PR-quadratic Finsler metrics, called SPR-quadratic Finsler metrics, which is closed under projective changes with respect to a fixed volume form on M. This class contains the class of Douglas-Weyl metrics and is a subset of the class of Weyl metrics. The paper shows that any SPR-quadratic Finsler metric has a scalar flag curvature and a PR-quadratic Finsler metric has a scalar curvature if and only if it is of SPR-quadratic type. The results presented in this paper contribute to a deeper understanding of the behavior of PR-quadratic Finsler metrics and provide insights into the geometric properties of these metrics.

Keywords

References

  • 1. H. Akbar-Zadeh, Sur les espaces de Finsler ´a courbures sectionnelles constantes, Bulletins
    de l’Academie Royale de Belgique, 5e S´erie - Tome LXXXIV (1988), No. 10, 281-322.
  • 2. PL. Antonelli, RS. Ingarden and M. Matsumoto, The Theorey of Sprays and Finsler
    Spaces with Applications in Physics and Biology, Kluwer Academic Publishers, (1993).
  • 3. S. B´acs´o and I. Papp, A note on generalized Douglas space, Period. Math. Hungarica, 48
    (2004), No. 1-2, 181-184.
  • 4. X. Cheng and Z. Shen, On Douglas metrics, Publ. Math. Debrecen, 66 (2005), No. 3-4,
    503-512.
  • 5. X. Cheng and Z. Shen, Finsler Geometry: An Approach via Randers Spaces, SpringerVerlag, (2011).
  • 6. N. Sadeghzadeh, On Finsler metrics of quadratic curvature, Journal of Geometry and
    Physics, 132 (2018), 75-83.
  • 7. Z. Shen, On Finsler geometry of submanifolds, Math. Annalen, 311 (1998), 549-576.
  • 8. Z. Shen, Differential Geometry of Spray and Finsler Spaces, Kluwer Aca-demic Publishers
    (2001).
  • 9. Z. Shen, On some non-Riemannian quantities in Finsler geometry, Canad. Math. Bull.
    56 (2013), No. 1, 184-193.
  • 10. C. Yu and H. Zhu, On a new class of Finsler metrics, Differ. Geom. Appl. 29 (2011),
    No. 2, 244-254.
Journal of Finsler Geometry and its Applications
Volume 5, Issue 1
2024
Pages 115-126

Files

Share

How to cite

Statistics