Acknowledgement
The authors would like to thank the anonymous referees for their useful suggestions. The authors would like to thank professor Akbar Tayebi for his technical assistance with Maple software.
References
- P. L. Antonelli, R. S. Ingarden and M. Matsumoto, The theory of sprays and Finsler spaces with applications in physics and biology, 58(1993), Kluwer Academic Publishers, Dordrecht.
- G. S. Asanov, Conformal property of the Finsler space FSR and extension of electromagnetic field equations, Rep. Math. Phys., 45(2)(2000), 155-169. https://doi.org/10.1016/S0034-4877(00)89029-1
- S. Bacso and X. Cheng, Finsler conformal transformations and the curvature invariances, Publ. Math. Debrecen, 70(2007), 221-231. https://doi.org/10.5486/PMD.2007.3606
- D. Bao, S. S. Chern and Z. Shen, An Introduction to Riemann-Finsler geometry, Grad. Texts in Math. 200, Springer-Verlag, New York, (2000).
- D. Bao and C. Robles, Ricci and flag curvatures in Finsler geometry, in a Sampler of Finsler Geometry, Math. Sci. Res. Inst. Publ., 50(2004), 197-259.
- G. Chen and X. Cheng, An important class of conformally flat weak Einstein Finsler metrics, Internat. J. Math., 24(1)(2013), 1350003.
- X. Cheng, H. Wang and M. Wang, (α, β)-metrics with relatively isotropic mean Landsberg curvature, Publ. Math. Debrecen, 72(34)(2008), 475-485. https://doi.org/10.5486/PMD.2008.4073
- S. S. Chern and Z. Shen, Riemann-Finsler Geometry, Nankai Tracts Math., 6(2005), World Scientific Publishing Co. Pte. Ltd., Hackensack.
- M. Hashiguchi, On conformal transformations of Finsler metrics, J. Math. Kyoto Univ., 16(1976), 25-50.
- Y. Ichijyo and M. Hashuiguchi, On the condition that a Randers space be conformally flat, Rep. Fac. Sci. Kagoshima Univ. Math. Phys. Chem., 22(1989), 7-14.
- L. Kang, On conformally flat Randers metrics, Sci. Sin. Math., 41(2011), 439-446. https://doi.org/10.1360/012010-910
- V. K. Kropina, On projective two-dimensional Finsler spaces with special metric, Trudy Sem. Vektor. Tenzor. Anal., 11(1961), 277-292, (in Russian).
- H. Rund, The Differential Geometry of Finsler Spaces, Springer-Verlag, Berlin, (1959).
- S. Saberali and B. Rezaei1, On conformal transformations of general (α, β)-metrics, Bull. Iranian Math. Soc. 47(4)(2021), 1173-1185. https://doi.org/10.1007/s41980-020-00434-1
- Y. Shen and Z. Shen, Introduction to Modern Finsler Geometry, World Scientific Publishing Company, Singapore, (2016).
- H. Shimada and S. V. Sabau, Introduction to Matsumoto metric, Nonlinear Analy.: Theo., Math. & Appl., 63(5-7)(2005), 165-168.
- A. Tayebi and M. Amini, On Conformally flat exponential (α, β)-metrics, Proc. Nat. Acad. Sci. India Sect. A, 92(3)(2022), 353-365. https://doi.org/10.1007/s40010-021-00767-4
- A. Tayebi and M. Razgordani, On conformally flat fourth root (α, β)-metrics, Differential Geom. Appl., 62(2019), 253-266. https://doi.org/10.1016/j.difgeo.2018.12.002
- A. Tayebi, M. Razgordani and B. Najafi, On conformally flat cubic (α, β)-metrics, Vietnam J. Math., 49(4)(2021), 987-1000. https://doi.org/10.1007/s10013-020-00389-0
- R. Yoshikawa and S. V. Sabau, Kropina metrics and Zermelo navigation on Riemannian manifolds, Geom. Dedicata, 171(1)(2014), 119-148. https://doi.org/10.1007/s10711-013-9892-8