On the L-duality of a Finsler space with special (α, β) metric

R. Miron initiated the study of L-duality in Lagrange and Finsler spaces in ۱۹۸۷. The concrete L-duals of the Randers metric, Kropina metric, Matsumoto metric, exponential metric, as well as a few more unique (α, β)-metrics, are really just an of the remarkable results obtained. The importance of L-duality, however, is basically limited to finding the dual of a few key Finsler functions.In this paper, we find L-dual of a Finsler space with a special (α, β)-metric F=\frac{(\alpha+\beta)^۳}{\alpha^۲}, where α is a Riemannian metric and β is a differential one form.

Keywords:

Finsler space , Cartan space , L- Dulity between Finsler and Cartan Spaces