University of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201On semi C-reducible Finsler spaces130142124610.22098/jfga.2020.1246ENAbbas HeydariDepartment of Pure Mathematics,
Faculty of Mathematical Sciences, Tarbiat Modares University,
Tehran, Iran
E-mail: aheydari@modares.ac.irJournal Article20210712In this paper, we study the class of semi-C-reducible Finsler manifolds. Under a condition, we prove that every semi-C-reducible Finsler spaces with a semi-P-reducible metric has constant characteristic scalar along Finslerian geodesics or reduces to a Landsberg metric. By this fact, we characterize the class of semi-P-reducible spaces equipped with an (α, β)-metric. More precisely, we proved that such metrics are Berwaldian B= 0,or have vanishing S-curvature S= 0 or satisfy a well-known ODE. This yields an extension of Tayebi-Najafi’s classification for 3-dimensional (α, β)-metric of Landsberg-type.https://jfga.uma.ac.ir/article_1246_ab56439a0afbfde0c3c80bf897a6623a.pdf