On semi C-reducible Finsler spaces

Document Type : Original Article

Author

Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran E-mail: aheydari@modares.ac.ir

Abstract

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= 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.

Keywords

References

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Journal of Finsler Geometry and its Applications
Volume 1, Issue 2
December 2020
Pages 130-142

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