On the ℒ-duality of a Finsler space with exponential metric αe^β/α

The (α, β)-metrics are the most studied Finsler metrics in Finsler geometry with Randers, Kropina and Matsumoto metrics being the most explored metrics in modern Finsler geometry. The ℒ-dual of Randers, Kropina and Matsumoto space have been introduced in [3, 4, 5], also in recent the ℒ-dual of a Finsler space with special (α, β)-metric and generalized Matsumoto spaces have been introduced in [16, 17]. In this paper, we find the ℒ-dual of a Finsler space with an exponential metric αe^β/α, where α is Riemannian metric and β is a non-zero one form.