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Push-Forwards and Pull-Backs

  • Jon Pierre Fortney
Chapter
  • 3.1k Downloads

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.

References

  1. 4.
    David Bachman. A Geometric Approach to Differential Forms. Birkhäuser, 2006.Google Scholar
  2. 12.
    R.W.R. Darling. Differential Forms and Connections. Cambridge University Press, 1994.Google Scholar
  3. 18.
    Harold Edwards. Advanced Calculus: A Differential Forms Approach. Birkhäuser, 1969.Google Scholar
  4. 27.
    John Hubbard and Barbara Hubbard. Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach. Matrix Editions, 4th edition, 2009.Google Scholar
  5. 31.
    Jarrold Marsden and Michael Hoffman. Elementary Classical Analysis. W.H. Freeman and Company, 2 edition, 1993.Google Scholar
  6. 36.
    Barrett O’Neill. Elementary Differential Geometry. Academic Press, 2 edition, 2006.Google Scholar
  7. 37.
    Paul Renteln. Manifolds, Tensors, and Forms. Cambridge University Press, 2014.Google Scholar
  8. 43.
    James Stewart. Calculus. Brooks/Cole Cengage Learning, 6 edition, 2009.Google Scholar
  9. 46.
    Loring Tu. An Introduction to Manifolds. Springer, 2 edition, 2010.Google Scholar

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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