INTRINSIC THEORY OF Cv-REDUCIBILITY IN FINSLER GEOMETRY

In the present paper, following the pullback approach to
Finsler geometry, we study intrinsically the Cv-reducible and generalized
Cv-reducible Finsler spaces. Precisely, we introduce a coordinate-free
formulation of these manifolds. Then, we prove that a Finsler manifold is Cv-reducible if and only if it is C-reducible and satisfies the Tcondition. We study the generalized Cv-reducible Finsler manifold with
a scalar π-form A. We show that a Finsler manifold (M, L) is generalized Cv-reducible with A if and only if it is C-reducible and T = A.
Moreover, we prove that a Landsberg generalized Cv-reducible Finsler
manifold with a scalar π-form A is Berwaldian. Finally, we consider a special Cv-reducible Finsler manifold and conclude that a Finsler manifold is a special Cv-reducible if and only if it is special semi-C-reducible
with vanishing T-tensor.