Let (M, g) be a Finsler manifold, TM0 its slit tangent bundle with complete lift metric ˜g. Then every complete lift projective vector field on (TM0, ˜g), is an affine vector field. Moreover, if (M, g) is a Landsberg space, then there is a one-to-one correspondence between complete lift projective vector fields on (TM0, ˜g) and affine vector fields on (M, g).
