In mathematics, particularly differential topology, the secondary vector bundle structurerefers to the natural vector bundle structure on the total space TE of the tangent bundle of a smooth vector bundle , induced by the push-forward p∗ : TE → TM of the original projection map p : E → M.This gives rise to a double vector bundle structure.
In the special case = , where TE = TTM is the double tangent bundle, the secondary vector bundle ∗, TM] is isomorphic to the tangent bundle of TM through the canonical flip.