Manifolds and Forms on Manifolds

  • Jon Pierre Fortney


In this chapter we reintroduce manifolds in a somewhat more mathematically rigorous manor while simultaneously trying not to overwhelm you with details. As always we will still place an emphasis on conceptual understanding and the big picture. Manifold theory is a vast and rich subject and there are numerous books that present manifolds in a completely rigorous manor with all the gory technical details made explicit. When you understand this chapter you will be prepared to tackle these texts.


  1. 5.
    Richard Bishop and Richard Crittenden. Geometry on Manifolds. Academic Press, 1964.Google Scholar
  2. 10.
    Lawrence Conlon. Differentiable Manifolds. Birkhäuser, 2 edition, 2001.Google Scholar
  3. 14.
    Manfredo do Carmo. Riemannian Geometry. Birkhäuser, 1992.Google Scholar
  4. 33.
    Daniel Martin. Manifold Theory. Harwood Publishing, 2002.Google Scholar
  5. 35.
    James Munkres. Analysis on Manifolds. Addison-Wesley Publishing Company, 1991.Google Scholar
  6. 37.
    Paul Renteln. Manifolds, Tensors, and Forms. Cambridge University Press, 2014.Google Scholar
  7. 47.
    Gerard Walschap. Multivariable Calculus and Differential Geometry. De Gruyter, 2015.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

Personalised recommendations