Using the Grifone formalism of the connection Γ[8] and the notations of Frölicher-Nijenhuis [4], for a Finsler manifold we establish that there exists a tensor W invariant under the projective transformation and that the curvature R of the homogenous Grifone-Ehersmann connection can be written as  if and only if the tensor W vanishes, where ω and π are semi-basic forms, J is the vertical endomorphism and C is the Liouville vector field.

Finsler manifold, homogenous connection, spray, curvature, projective transformation.