On Two-Dimensional Landsberg Space with a Special \((α,β)\)-Metric - Shanker, Gauree; Choudhary, Deepti (Communications in Mathematics and Applications, 2017)
The purpose of the present paper is to study a Finsler space with a special \((α,β)\)-metric \(L(α,β) =α+β+κ\dfrac{β^2}{α}\) \((ε\) and \(k eq 0\) are real constants) satisfying some conditions. First we find a condition for a Finsler space with a special \((α,β)\)-metric to be a Berwald space. Then we show that if a two-dimensional Finsler space with a special \((α,β)\)-metric \(L(α,β) =α+β+κ\dfrac{β^2}{α}\) \((ε\) and \(k eq 0\) are real constants) is a Landsberg space, then it is a Berwald space.