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the second map by the diagonal yields the canonical vector field.

If are local coordinates for , the vector field has the expression

:

More concisely, - the first pair of coordinates do not change because it is the section of a bundle and these are just the point in the base space: the last pair of coordinates are the section itself. This expression for the vector field depends only on , not on , as only the tangent directions can be naturally identified.

Alternatively, consider the scalar multiplication function:

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