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In mathematics, particularly differential topology, the secondary vector bundle structure refers 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 of the original projection map . This gives rise to a double vector bundle structure . In the special case , where is the double tangent bundle, the secondary vector bundle is isomorphic to the tangent bundle of through the canonical flip. == Construction of the secondary vector bundle structure == Let be a smooth vector bundle of rank . Then the preimage of any tangent vector in in the push-forward of the canonical projection is a smooth submanifold of dimension , and it becomes a vector space with the push-forwards : of the original addition and scalar multiplication : as its vector space operations. The triple becomes a smooth vector bundle with these vector space operations on its fibres. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「secondary vector bundle structure」の詳細全文を読む スポンサード リンク
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