This paper is a continuation of previous papers [5] and [6] by the same author. In [6] the induced connection coefficients which appear in (1.13), (1.14) and (1.15) are determined under conditions when $\bar D\ell^d$ and $\bar D\ell^k$ are defined by (1.18) and (1.19). In [6] it is proved that the mentioned formulae are consistent with each other only when relation (1.21) is satisfied. This condition is satisfied in the several cases. In this paper we shall examine the special case when $B^\alpha_a=B\alpha_a(x)$ and $N^\alpha_k=N^\alpha_k(x)$ i.e. when $B^\alpha_a$ and $N^\alpha_k $ are not functions of $\dot x$. Since we suppose (1.1) i.e. that $g_{\alpha\beta}(x,\dot x)B^\alpha_a(x) N^\alpha_k (x)=0$ so our examination is restricted only to those Finsler spaces in which the metric tensor has such a special form that relation (1.1) is valid. Let us denote such Finsler spaces by $\bar F_n$. The curvature tensors in $\bar F_n$ are defined by (2.5), (2.6) and (2.7). In this paper the relations between alternated differentials of a vector field and the curvature tensors are given. The curvature tensors and their alternated differentials are decomposed in the direction of vectors $B^\alpha_a$ and $N^\alpha_k $.