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Text on differential geometry

  1. Jul 30, 2004 #1


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    I was hoping if somebody could point me to a starters text on differential geometry. I have done some calculas ~4 years ago - I can refresh stuff as I need to. My physics is at high school level, but I do read up on stuff every once a while

    My aim in learning diff geom is to be able to understand a mathematical treatment of GTR.

  2. jcsd
  3. Jul 30, 2004 #2
    Here is a discussion with some helpful information:

  4. Jul 30, 2004 #3
    If I were you then I'd get

    Tensors, Differential Forms, and Variational Principles, Lovelock & Rund, Dover Pub., (1989)

    Differential Geometry, Kreyszig, Dover Pub., (1991)

    There is Introduction to Tensor Calculus and Continuum Mechanics which is online at the bottom of

    My favorite is Lovelock. But if your goal is to learn GR then learn it as you learn GR. By the text A first course in general relativity, Bernard F. Schutz, Cambridge Univ. Press, (1990). Its an excellant text. I learned GR from it and I didn't know much differential geometry before I started.

  5. Jul 30, 2004 #4


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  6. Jul 31, 2004 #5
  7. Jul 31, 2004 #6


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  8. Aug 5, 2004 #7


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    I'm going to answer your question with a question.

    How's your algebra?

    I can tell you from personal experience that if you don't have a solid understanding of linear algebra, differential geometry is going to seem _much_ harder than it needs to be. "Some calculus" usually implies very little algebra, since that typically comes after calculus in the curriculum.

    If you don't have a solid algebra background, I'd strongly suggest picking up one or two algebra texts and working through as much of it as you can force yourself to do, and I'd suggest doing it before hitting the differential geometry.

    There are many algebra books, but if you want a recommendation, I've found Michael Artin's "Algebra" to be readable, accessible, and useful. (And I'm not working for Artin, really, even though I've recommended this text a few other times in other forums!)

    Just as one simple example, if you already know what a "bilinear form" is before you first encounter the metric tensor, you won't feel quited so bushwhacked by it all.

    And finally, differential geometry can be learned from GR texts, as well as from math texts. The authors often assume tensor calculus is new to the reader, and so they explain it as they go -- but not so the algebra!
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