In a Finsler manifold provided with a linear connection Γ^i_(x), a Finsler connection such as Γ^*={Γ^i_(x), Γ^i_(x)y^l, C^i_} can be considered, where C^i_=1/2g^ ∂_mg_. The connection Γ^* is called the Finsler connection associated with Γ^i_(x). In this case, the A-covariant derivative ▽k, v-covariant derivative ▽k and the hv-curvature tensor P^h_, which have been defined by Matsumoto [8], can be also considered
