On Two-Dimensional Landsberg Space with a Special \((\alpha,\beta)\)-Metric

Gauree Shanker, Deepti Choudhary


The purpose of the present paper is to study a Finsler space with a special \((\alpha,\beta)\)-metric \(L(\alpha,\beta) =\alpha+\beta+\kappa\dfrac{\beta^2}{\alpha}\) \((\epsilon\) and \(k\neq 0\) are real constants) satisfying some conditions. First we find a condition for a Finsler space with a special \((\alpha,\beta)\)-metric to be a Berwald space. Then we show that if a two-dimensional Finsler space with a special \((\alpha,\beta)\)-metric \(L(\alpha,\beta) =\alpha+\beta+\kappa\dfrac{\beta^2}{\alpha}\) \((\epsilon\) and \(k\neq 0\) are real constants) is a Landsberg space, then it is a Berwald space.


Berwald space; Cartan connection; Finsler space; Landsberg space; Main scalar

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