It is defined by F ∗ ∗ ( α α ) ( X 1 , X 2 , … … , X k ) = α α ( F ∗ ∗ X 1 , F ∗ ∗ X 2 , … … , F ∗ ∗ X k ) , where the subscript star denotes the pushforward of the map F, and X, X, …, X are vectors in T p M. (This is in accord with what was detailed about the pullback of the inclusion map. In the general case here, one cannot proceed as simply because F ∗ X 1 ≠ X 1 in general.)