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What are the books in Differential Geometry with a good collection of problems? At present I am having John M. Lee's Riemannian Manifolds, Kobayashi & Nomizu's Foundations of Differential Geometry. I particularly like Dieudonne's books in Analysis as well as books like Alexander Kirillov's Functional Analysis. To be precise, the books that have a huge number of exercises. The books I mentioned are definitely not of that category. Can anyone please suggest differential geometry books that gives a lot of exercises?

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  • $\begingroup$ Petersen's Riemanninan Geometry. $\endgroup$
    – M.B.
    Commented Jan 22, 2013 at 12:54
  • $\begingroup$ Related to my answer here $\endgroup$
    – Yuri Vyatkin
    Commented Jan 22, 2013 at 21:20

6 Answers 6

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This book (Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers) contains detailed solutions to 375 core exercises on differentiable manifolds, Lie groups, fiber bundles, and Riemannian geometry. It should be helpful to anyone who needs to aquire a solid working technique in these fields and to students who have problems to illustrate concepts, methods, and theorems by examples.

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The following list contains books on Differential Geometry with many, many exercises with solutions:

  • Tu, Introduction to Manifolds
  • Jänich, Vector Analysis
  • Gadea et al, Analysis and Algebra on Differential Manifolds, Workbook with Solutions
  • Lafontaine, An Introduction to Differential Manifolds
  • Mishchenko & Fomenko, Problems in Differential Geometry and Topology
  • Aubin, A Course in Differential Geometry
  • Barden & Thomas, An Introduction to Differential Manifolds
  • Morita, Geometry of Differential Forms

Hope it helps.

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John M. Lee's Introduction to Smooth Manifolds is also a great book with lots of exercises.

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  • $\begingroup$ Can you suggest one for beginning undergraduates which has some applications to physics? $\endgroup$
    – Manjil P. Saikia
    Commented Jun 19, 2013 at 8:04
  • $\begingroup$ I am not aware of such a book. Try this question for potential suggestions. $\endgroup$
    – Michael Albanese
    Commented Jun 19, 2013 at 8:25
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Barrett O'Neill's book "Elementary Differential Geometry" is really good. He has tons of exercises and he's a mathematical physicists/ diff. geometer so there you go. He also has a text on black holes and another text called "Semi-Riemannian Geometry" (tons of physics applications, problems).

$\textbf{Update}$: Loring Tu also has a differential geometry book now.

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Andrew Pressley's Elementary Differential Geometry. This book is a very good book for beginners. It has quite an amount of exercises and with answers from within the book.

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Spivak's Introduction to Differential Geometry

https://www.maa.org/press/maa-reviews/a-comprehensive-introduction-to-differential-geometry-vol-i

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  • $\begingroup$ Well, after Volume I the exercises peter off pretty seriously. $\endgroup$
    – Ted Shifrin
    Commented Apr 9, 2017 at 5:21
  • $\begingroup$ Link is dead... $\endgroup$
    – Cheng
    Commented Apr 6, 2022 at 5:45
  • $\begingroup$ @Cheng Changed the link thanks. (You could have edited.) $\endgroup$
    – Ethan Bolker
    Commented Apr 6, 2022 at 14:18

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