In this paper, we investigate the mean Landsberg curvature of two subclasses of (α,β)-metrics. We prove that these subclasses of (α,β)-metrics with vanishing mean Landsberg curvature have vanishing S-curvature. Using it, we prove that these Finsler metrics are weakly Landsbergian if and only if they are Berwaldian.
1. M Atashafrouz, Characterization of 3-dimensional left-invariant locally projectively flat Randers metrics, Journal of Finsler Geometry and its Applications.1(1) (2020), 96-102.
2. S. B´acs´o, X. Cheng and Z. Shen, Curvature properties of (α, β)-metrics, Adv. Stud. Pure. Math, Mathematical Society of Japan, 48(2007), 73-110.
3. X. Cheng and Z. Shen, A class of Finsler metrics with isotropic S-curvature, Israel J. of Math. 169(1)(2009), 317–40.
4. S. S. Chern and Z. Shen, Riemann-Finsler geometry, World Scientific, 2005.
5. B. Li and Z. Shen, On a class of weakly Landsberg Metrics, Science in China, Series A, 50(2007), 75-85.
6. B. Najafi and A. Tayebi, Some curvature properties of (α, β)-metrics, Bull. Math. Soc. Sci. Math. Roumanie, Tome 60 (108) No. 3, (2017), 277-291
Majidi, J., & Haji-Badali, A. (2023). Two classes of weakly Landsberg Finsler metrics. Journal of Finsler Geometry and its Applications, 4(2), 92-102. doi: 10.22098/jfga.2023.13773.1103
MLA
Jila Majidi; Ali Haji-Badali. "Two classes of weakly Landsberg Finsler metrics", Journal of Finsler Geometry and its Applications, 4, 2, 2023, 92-102. doi: 10.22098/jfga.2023.13773.1103
HARVARD
Majidi, J., Haji-Badali, A. (2023). 'Two classes of weakly Landsberg Finsler metrics', Journal of Finsler Geometry and its Applications, 4(2), pp. 92-102. doi: 10.22098/jfga.2023.13773.1103
VANCOUVER
Majidi, J., Haji-Badali, A. Two classes of weakly Landsberg Finsler metrics. Journal of Finsler Geometry and its Applications, 2023; 4(2): 92-102. doi: 10.22098/jfga.2023.13773.1103
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