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The functor taking each manifold to its tangent bundle is an example of a section of this bundle object.
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Let be a subbundle of the tangent bundle of.
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See also tangent bundle and cotangent bundle.
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In connection with foliation theory, a subbundle of the tangent bundle of a smooth manifold may be called a distribution (of tangent vectors).
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Important examples of vector bundles include the tangent bundle and cotangent bundle of a smooth manifold.
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Fundamental examples are the holomorphic tangent bundle of a complex manifold, and its dual, the holomorphic cotangent bundle.
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The collection of tangent spaces at all points can in turn be made into a manifold, the tangent bundle, whose dimension is 2 "n".
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