In this paper, we consider the class of L-reducible Finsler metrics which contains the class of C-reducible metrics and the class of Landsberg metrics. Let (M,F) be a 3-dimensional L-reducible Finsler manifold. Suppose that F has a relatively isotropic mean Landsberg curvature. We find a condition on the main scalars of F under which it reduces to a Randers metric or a Landsberg metric.
1. M. Atashafrouz , Characterization of 3-dimensional left-invariant locally projectively flat Randers metrics, Journal of Finsler Geometry and its Applications, 1(2020), 96-102.
2. M. Z. Laki, On generalized symmetric Finsler spaces with some special (α, β)-metrics, Journal of Finsler Geometry and its Applications, 1(2020), 45-53.
3. M. Matsumoto and S. H¯oj¯o, A conclusive theorem for C-reducible Finsler spaces, Tensor. N. S. 32(1978), 225-230.
4. M. Matsumoto and C. Shibata, On semi-C-reducibility, T-tensor and S4-1ikeness of Finsler spaces, J. Math. Kyoto Univ. 19(1979), 301-314.
5. M. Matsumoto, Theory of Finsler spaces with (α, β)-metric, Rep. Math. Phys. 31(1992), 43-84.
6. M. Matsumoto, On Finsler spaces with Randers metric and special forms of important tensors, J. Math. Kyoto Univ. 14(1974), 477-498.
7. M. Matsumoto and H. Shimada, On Finsler spaces with the curvature tensors Phijk and Shijk satisfying special conditions, Rep. Math. Phys. 12(1977), 77-87.
8. A. Mo´or, Uber die Torsion-Und Krummungs invarianten der drei reidimensionalen ¨ Finslerchen R¨aume, Math. Nach, 16(1957), 85-99.
9. T. Rajabi, On the norm of Cartan torsion of two classes of (α, β)-metrics, Journal of Finsler Geometry and its Applications, 1(2020), 66-72.
10. Y. Takano, On the theory of fields in Finsler spaces, Intern. Symp. Relativity and Unified Field Theory, Calcutta, 1975.
11. A. Tayebi, M. Bahadori and H. Sadeghi, On spherically symmetric Finsler metrics with some non-Riemannian curvature properties, J. Geom. Phys. 163 (2021), 104125.
12. A. Tayebi and M. Barzegari, Generalized Berwald spaces with (α, β)-metrics, Indagationes Mathematicae, 27(2016), 670-683.
13. A. Tayebi and B. Najafi, On homogeneous Landsberg surfaces, J. Geom. Phys. 168(2021), 104314.
14. A. Tayebi and B. Najafi, Classification of 3-dimensional Landsbergian (α, β)-mertrics, Publ. Math. Debrecen, 96(2020), 45-62.
15. A. Tayebi and M. Razgordani, On conformally flat fourth root (α, β)-metrics, Differ. Geom. Appl. 62(2019), 253-266.
16. A. Tayebi and H. Sadeghi, Generalized P-reducible (α, β)-metrics with vanishing Scurvature, Ann. Polon. Math. 114(1) (2015), 67-79.
17. A. Tayebi and H. Sadeghi, On generalized Douglas-Weyl (α, β)-metrics, Acta. Math. Sinica. English. Series. 31(2015), 1611-1620.
Beizavi, S. (2020). On L-reducible Finsler manifolds. Journal of Finsler Geometry and its Applications, 1(2), 73-82. doi: 10.22098/jfga.2020.1241
MLA
Beizavi, S. . "On L-reducible Finsler manifolds", Journal of Finsler Geometry and its Applications, 1, 2, 2020, 73-82. doi: 10.22098/jfga.2020.1241
HARVARD
Beizavi, S. (2020). 'On L-reducible Finsler manifolds', Journal of Finsler Geometry and its Applications, 1(2), pp. 73-82. doi: 10.22098/jfga.2020.1241
CHICAGO
S. Beizavi, "On L-reducible Finsler manifolds," Journal of Finsler Geometry and its Applications, 1 2 (2020): 73-82, doi: 10.22098/jfga.2020.1241
VANCOUVER
Beizavi, S. On L-reducible Finsler manifolds. Journal of Finsler Geometry and its Applications, 2020; 1(2): 73-82. doi: 10.22098/jfga.2020.1241
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