Abstract
In this chapter we introduce two extremely important concepts, the push-forward of a vector and the pull-back of a differential form. In section one we take a close look at a simple change of coordinates and see what affect this change of coordinates has on the volume of the unit square. This allows us to motivate the push-forward of a vector in section two. Push-forwards of vectors allow us to move, or “push-forward,” a vector from one manifold to another. In the case of coordinate changes the two manifolds are actually the same manifold, only equipped with different coordinate systems.
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Fortney, J.P. (2018). Push-Forwards and Pull-Backs. In: A Visual Introduction to Differential Forms and Calculus on Manifolds. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-96992-3_6
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DOI: https://doi.org/10.1007/978-3-319-96992-3_6
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-96991-6
Online ISBN: 978-3-319-96992-3
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