On The L – Duality of a Finsler Space with Special Metric

During the study of this paper, we have to study R. Miron’s concept of L-duality in Lagrange and Finsler spaces in [1987]. We have continued this study, and here we give some special conditions for the same theory. The factual L-duals of the Randers metric, Kropina metric, Matsumoto metric, exponential metric, as well as some more unique metrics, are really just some of the extraordinary 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 the L-dual of a Finsler space with a special (α, β)-metric F = (α + β² /α), where α is a Riemannian metric and β is a differential one-form. 2010MSC: 53B40 & 53C60