Abstract
In this paper, we discuss about the conformal complex Landsberg spaces with some of theirs important subclasses. The study is made with respect to the complex linear connections: Chern-Finsler, Berwald and Rund. The function ρ between conformal Landsberg (G – or strong – Landsberg) spaces (M,L) and (M, L) must be constant unless the spaces are purely Hermitian. A special approach is devoted to the projective generalized Berwald manifolds and to the conformal projective complex Berwald spaces, in particular. Mathematics Subject Classification 2000: 53B40, 53C60.
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