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We show how to compute tensor derivatives and curvature tensors using affineconnections. This allows for all computations to be obtained without usingcoordinate systems, in a way that parallels the computations appearing inclassical Riemannian Geometry. In particular, we obtain Bianchi identities forthe curvature tensor of any anisotropic connection, we compare the curvaturetensors of any two anisotropic connections, and we find a family of anisotropicconnections which are well suited to study the geometry of Finsler metrics.

Curvature computations in Finsler Geometry using a distinguished class of anisotropic connections