On the Finsler Connection Associated with a Linear Connection Satisfying P^h_ =0

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.