**Higher-order Tangent Bundles**

Since the tangent bundle is itself a smooth manifold, the second-order tangent bundle can be defined via repeated application of the tangent bundle construction:

In general, the th-order tangent bundle can be defined recursively as .

A smooth map has an induced derivative, for which the tangent bundle is the appropriate domain and range . Similarly, higher-order tangent bundles provide the domain and range for higher-order derivatives .

A distinct but related construction are the jet bundles on a manifold, which are bundles consisting of jets.

Read more about this topic: Tangent Bundle

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