On R−complex Finsler spaces

In the present paper we submit for study a new class of Finsler spaces. Through restricting the homogeneity condition from the definition of a complex Finsler metric to real scalars, λ ∈ R, is obtained a wider class of complex spaces, called by us the R−complex Finsler spaces. Two subclasses are taken in consideration: the Hermitian and the non-Hermitian R−complex Finsler spaces. In an R−complex Finsler space we determine a nonlinear connection from the variational problem similar as in the complex Lagrange geometry ([11]) for the Hermitian case and similar as in the real Lagrange geometry ([5, 7, 9]) for the non-Hermitian case. There are studied the N− complex linear connections in each of two classes. M.S.C. 2000: 53B40, 53C60.