Abstract: In this paper we study the two-dimensional complex Finsler spaces with $(\alpha ,\beta )$-metrics by using the complex Berwald frame. A special approach is dedicated to the complex Berwald spaces with $(\alpha ,\beta )$ - metrics. We establish the necessary and sufficient condition so that the complex Randers and Kropina spaces should be complex Berwald spaces, and we will illustrate the existence of these spaces in some examples.
Keywords: Berwald frame, complex Landsberg space, complex Berwald space, complex Finsler spaces with $(\alpha ,\beta )$-metrics
Classification (MSC2000): 53B40; 53C60
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