On semi C-reducible Finsler spaces

In 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= ۰,or have vanishing S-curvature S= ۰ or satisfy a well-known ODE. This yields an extension of Tayebi-Najafi’s classification for ۳-dimensional (α, β)-metric of Landsberg-type.

Keywords:

P-reducible space , ۳-dimensional Finsler space , weakly Landsberg metric