On quintic (α,β)-metrics in Finsler geometry

Document Type : Original Article


1 Department of Mathematics Basic Sciences Faculty University of Bonab, Bonab, Iran

2 Department of Mathematics, Basic Sciences Faculty, University of Bonab, Bonab 5551395133, Iran.


Abstract. In this paper, we study the class of quintic (α,β)-metrics. We show that every weakly Landsberg 5-th root (α,β)-metrics has vanishing S-curvature. Using it, we prove that a quintic (α,β)-metric is a weakly Landsberg metric if and only if it is a Berwald metric. Then, we show that a quintic (α,β)-metric satisfies Ξ = 0 if and only if S = 0.