CONFORMAL COMPLEX LANDSBERG SPACES

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 rho between conformal Landsberg (G - or strong - Landsberg) spaces (M, L) and (M, (L) over tilde) 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.