High Quality Content by WIKIPEDIA articles! In mathematics, particularly differential topology, the secondary vector bundle structure refers to the natural vector bundle structure (TE,p*,TM) on the total space TE of the tangent bundle of a smooth vector bundle (E,p,M), induced by the push-forward p*:TE?TM of the original projection map p:E?M.In the special case (E,p,M)=(TM,?TM,M), where TE=TTM is the double tangent bundle, the secondary vector bundle (TTM,(?TM)*,TM) is isomorphic to the tangent bundle (TTM,?TTM,TM) of TM through the canonical flip. if and only if the connector map is linear with respect to the secondary vector bundle structure (TE,p*,TM) on TE. Then the connection is called linear. Note that the connector map is automatically linear with respect to the tangent bundle structure (TE,?TE,E).

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