In this paper we study the two-dimensional complex Finsler spaces with (α, β)-metrics by using the complex Berwald frame. A special approach is dedicated to the complex Berwald spaces with (α, β) 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 som...

The study of moduli space and Teichmüller space has a long history. These two spaces lie in the intersections of the researches in many areas of mathematics and physics. Many deep results have been obtained in history by many famous mathematicians. Here we will only mention a few that are closely related to our discussions. Riemann was the first who considered the space M of all complex structu...

Abstract Finsler metrics are direct generalizations of Riemannian such that the quadratic indicatrices in tangent spaces a manifold replaced by more general convex bodies as unit spheres. A linear connection on base is called compatible with metric if induced parallel transports preserve Finslerian length vectors. manifolds admitting connections generalized Berwald Wagner (Dokl Acad Sci USSR (N...