On complex Landsberg and Berwald spaces

In this paper, we study complex Landsberg spaces and some of their important subclasses. The tools of this study are the Chern-Finsler, Berwald, and Rund complex linear connections. We introduce and characterize the class of generalized Berwald and complex Landsberg spaces. The intersection of these spaces gives the so-called G-Landsberg class. This last class contains two other kinds of complex Finsler spaces: strong Landsberg and G-Kahler spaces. We prove that the class of G-Kahler spaces coincides with complex Berwald spaces, in Aikou's (1996)[1] sense, and it is a subclass of the strong Landsberg spaces. Some special complex Finsler spaces with (alpha, beta)-metrics offer examples of generalized Berwald spaces. Complex Randers spaces with generalized Berwald and weakly Kahler properties are complex Berwald spaces. (C) 2011 Elsevier B.V. All rights reserved.