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Looking for Differential Geometry books

  1. Mar 17, 2014 #1
    I am Looking for some books about Differential Geometry,and I just begin to learn Differential Geometry,so who can introduce some books about Differential Geometry that suitable for Beginners to me,and tell me where can download the PDF document of the book.
    thanks
     
  2. jcsd
  3. Mar 17, 2014 #2

    micromass

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    If you're brand new to differential geometry, then you should start by learning about curves and surfaces. The prerequisities to this are (rigorous) calculus and linear algebra. Some books here are

    - https://www.amazon.com/Differential-Geometry-Curves-Surfaces-Manfredo/dp/0132125897
    - https://www.amazon.com/Elementary-Differential-Geometry-Undergraduate-Mathematics/dp/184882890X
    - https://www.amazon.com/Elementary-Differential-Geometry-Christian-228/dp/0521721490
    Or the very excellent free lecture notes by Shifrin:
    - http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf

    The topics you should definitely cover are Gaussian curvature, the theorema egregium, the Gauss-Bonnet theorem.

    After this, you can go for modern differential geometry. This requires a bit more prerequisites though. For example, you'll need to know basic real analysis, metric spaces and topology. One good book that teaches you the necessary topology is

    - https://www.amazon.com/Introduction-Topological-Manifolds-Graduate-Mathematics/dp/1441979395

    After that you can go to Lee's other books:

    https://www.amazon.com/Introduction-Smooth-Manifolds-Graduate-Mathematics/dp/1441999817
    and

    https://www.amazon.com/Riemannian-Manifolds-Introduction-Curvature-Mathematics/dp/0387983228
     
    Last edited by a moderator: May 6, 2017
  4. Mar 18, 2014 #3

    mathwonk

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    here is a free one that is written by a very skillful writer and accomplished geometer:
    I recommend it:
    http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf [Broken]
     
    Last edited by a moderator: May 6, 2017
  5. Mar 18, 2014 #4

    micromass

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    I already linked that.
     
    Last edited by a moderator: May 6, 2017
  6. Mar 19, 2014 #5

    mathwonk

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    ah yes! now i see it. i am glad you also like that one.
     
  7. Mar 19, 2014 #6
    i was reading this book , it is a good book , thanks
     
  8. Sep 9, 2014 #7
    Here is one with an emphasis on numerical methods of differential geometry (especially Chapter 5) with lots of source codes in C/C++:

    https://www.amazon.com/Computational-Geometry-Surfaces-Application-Analysis/dp/0646594044
     
    Last edited by a moderator: May 6, 2017
  9. Sep 10, 2014 #8
    William L. Burke: Applied Differential Geometry if you know some physics.
     
  10. Sep 10, 2014 #9
    Shlomo Sternberg: Curvature in Mathematics and Physics
     
  11. Sep 11, 2014 #10
    Not an introductory text. You really need to have some familiarity with differential geometry on manifolds to understand it.
     
  12. Sep 11, 2014 #11
    if you read his Advanced calculus book ,you'll get probably the prerequisites you need for it.
     
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