ℝ - complex Hermitian (α, β) - metrics

Abstract

In this paper, we extend the known results on ℝ-complex Hermitian Finsler spaces from [4], by the study of three special ℝ-complex Hermitian Finsler spaces with (α, β)-metrics. We characterize the ℝ-complex Hermitian Finsler versions of the Kropina metric, Matsumoto metric, and another special (α, β)-metric. Moreover, we find the conditions for two of these three ℝ-complex Hermitian Finsler spaces to be Berwald. Based on [4,5,6,7,8], we write some explicit examples.