On semi C-reducible Finsler spaces

Heydari, Abbas

doi:10.22098/jfga.2020.1246

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	On semi C-reducible Finsler spaces
Journal of Finsler Geometry and its Applications
دوره 1، شماره 2، اسفند 2020، صفحه 130-142 اصل مقاله (101.56 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2020.1246
نویسنده
Abbas Heydari^*
Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran E-mail: aheydari@modares.ac.ir
چکیده
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.
کلیدواژه‌ها
3-dimensional Finsler space؛ weakly Landsberg metric

مراجع
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On semi C-reducible Finsler spaces