On class of square Finsler metrics

Document Type : Original Article

Author

Department of mathematics, Faculty of basic sciences, University of Qom,Qom, Iran.

Abstract

In this paper, we remark some of the well-known curvature properties of square Finsler metrics. Then, we study weakly stretch square Finsler metrics.

Keywords


  • 1. R.V. Ambartzumian, A note on pseudo-metrics on the plane, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 37(1976), 145-155.
  • 2. R. Alexander, Planes for which the lines are the shortest paths between points, Illinois
    J. of Math., 22(1978), 177-190.
  • 3. L. Berwald, On Finsler and Cartan geometries III, Two-dimensional Finsler spaces with
    rectilinear extremals, Ann. of Math. 42(1941), 84-112.
  • 4. W. Blaschke, Integral geometrie 11: Zur Variationsrechnung, Abh. Math. Sem. Univ.
    Hamburg, 11(1936), 359-366.
  • 5. H. Busemann, Problem IV: Desarguesian spaces, in Mathematical Developments arising
    from Hilbert Problems, Proc. Symp. Pure Math. 28(1976), Amer. Math. Soc., Providence, RI, 131-141.
  • 6. G. Hamel, Uber die Geometrien, in denen die Geraden die K¨urtzesten sind ¨ , Math. Ann.
    57(1903), 231-264.
  • 7. Y. Li and X. Mo, On dually flat square metrics, Differ. Geom. Appl. 62(2019), 60-71.
  • 8. A.V. Pogorelov, Hilbert’s Fourth Problem, Winston & Wiley, New York, 1982.
  • 9. A. Rapcs´ak, Uber die bahntreuen Abbildungen metrisher R¨aume ¨.
  • 10. Z. Shen and G. Yang, On square metrics of scalar flag curvature, arXiv:1302.3156v1.
  • 11. Y. Shen and C. Yu, On Einstein square metrics, Publ. Math. Debrecen. 85(3-4) (2014),
    413-424.
  • 12. Z.I. Szab´o, Hilbert’s fourth problem, Adv. Math. 59(1986), 185-301.