Double Tangent Bundle
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Double Tangent Bundle

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In mathematics, particularly differential topology, the double tangent bundle or the second tangent bundle refers to the tangent bundle T2M=T(TM) of the tangent bundle TM of a smooth manifold M. The double tangent bundle arises in the study of connections and second order ordinary differential equations, i.e. (semi)spray structures on smooth manifolds. The double tangent bundle is closely related to the second order jet bundle, which is an object specifically designed to hold the "2nd order derivative information" of smooth functions on smooth manifolds. Given a smooth map f : M to N there is ...