Push-Forwards and Pull-Backs

  • Jon Pierre Fortney


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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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Jon Pierre Fortney
    • 1
  1. 1.Department of Mathematics and StatisticsZayed UniversityDubaiUnited Arab Emirates

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