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2-dimensional differentiable surfaces

  1. Apr 15, 2013 #1
    What is a good book on 2-dimensional surfaces (3-spheres, etc.)?

    I need to know about geodesics, etc.
  2. jcsd
  3. Apr 15, 2013 #2


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    Differential Geometry of Curves and Surfaces - Do Carmo.

    EDIT: By the way, 3-spheres aren't 2-surfaces embedded in ##\mathbb{R}^{3}##. As you could guess from the name, they are 3-manifolds.
    Last edited: Apr 15, 2013
  4. Apr 15, 2013 #3
    This is the classic on curves and surfaces! So I second it.

    Other nice books are Millman and Parker: https://www.amazon.com/Elements-Differential-Geometry-Richard-Millman/dp/0132641437
    and Oneill: https://www.amazon.com/Elementary-Differential-Geometry-Revised-Second/dp/0120887355/

    And then there is of course Lee: https://www.amazon.com/Introduction-Smooth-Manifolds-Graduate-Mathematics/dp/1441999817 But this is not a book you want to read now, start with more "classical differential geometry" first. If you're interested, then you should read this book eventually though.
  5. Apr 15, 2013 #4
    OK thanks a bunch! I took a course on differential geometry years ago and actually still have my copy of Do Carmo and I need to get re-acquainted with it for thesis reasons.
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