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Differential Geometry Book

  1. Jun 3, 2010 #1
    Hi everyone.

    I am a senior undergrad math major and I'm looking for a Differential Geometry book to self-study. I have studied most/all of the other undergrad topics: algebra; real and complex analysis; point-set topology; etc.
    Any recommendations? Thanks
  2. jcsd
  3. Jun 3, 2010 #2
    whatever book you try, make sure it cover the manifold approach, since its the very heart of geo-diff
  4. Jun 3, 2010 #3
    Elements of Differential Geometry by Millman & Parker. Covers the usual local and global theories of curves and surfaces as well as manifolds.
  5. Jun 4, 2010 #4
    Ok, thanks Daverz. Dr Carlson's review on amazon.com has convinced me to get this book. Can you recommend a book to follow this one?
  6. Jun 4, 2010 #5
    Differential Forms and Connections by R. W. R. Darling
    Differential Geometry: Curves - Surfaces - Manifolds by K├╝hnel
    Riemannian Geometry by do Carmo

    Or you could go more in the direction of manifolds, topology, or differential equations.
  7. Jun 4, 2010 #6


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    Introduction to smooth manifolds, by John M. Lee. And Riemannian manifolds: an introduction to curvature, by the same author. Both are excellent. The latter covers connections, covariant derivative, parallel transport and curvature. The former covers everything else: Manifolds, tensor fields, Lie groups, differential forms, integration on manifolds, etc.
  8. Jun 5, 2010 #7
    Thank-you Daverz and Fredrik. Looks like I have plenty of reading!
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