Suppose that is smooth. The differential of is a smooth map between the tangent bundles of and . This map is also denoted and called the pushforward. For any point and any , there is a well-defined pushforward vector in . However, the same is not true of a vector field. If is not injective, say because has two or more preimages, then the vector field may determine two or more distinct vectors in . If is not surjective, then will be a point at which does not determine any tangent vector at all. Since a vector field on determines, by definition, a unique tangent vector at every point of , the pushforward of a vector field does not always exist.