Secondary Vector Bundle Structure (Paperback)

PMHigh 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