• Stephen Bruce Sontz
Part of the Universitext book series (UTX)


This volume started out as notes in an attempt to help my students in a course on classical differential geometry. Not feeling constrained to use one particular text, I went off on my merry way introducing some of the basic structures of classical differential geometry (standard reference: [30]) that are used in physics. When the students requested specific references to texts, I would say that any one from a standard list of quite excellent texts would be fine. But my approach was not to be found in any one of them. Rather, the students had to search here and there in the literature and then try to piece it all together. So my notes were just that: a piecing together of things well known. However, in the spirit of the famous saying of Feynman (see Ref. [14]) noted above, some considerable part of the development of the subject is left for the reader to do in the exercises. Of course, in that same spirit, the reader should create explicitly all of the material presented here.


  1. 14.
    R.P. Feynman, Feynman’s office: The last blackboards, Phys. Today, 42, no. 2, (1989) 88.CrossRefGoogle Scholar
  2. 30.
    S. Kobayashi and K. Nozimu, Foundations of Differential Geometry, John Wiley \(\&\) Sons, Vol. I, 1963 and Vol. II 1969.Google Scholar
  3. 32.
    S. Lang, Fundamentals of Differential Geometry, Graduate Texts in Mathematics, Vol. 191, Springer, 1999.Google Scholar
  4. 33.
    J. Lee, Introduction to Smooth Manifolds, Graduate Texts in Mathematics, Vol. 218, Springer, 2003.Google Scholar
  5. 44.
    S.B. Sontz, Principal Bundles: The Quantum Case, Springer, 2015.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Stephen Bruce Sontz
    • 1
  1. 1.Centro de Investigación en Matemáticas, A.C.GuanajuatoMexico

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