Good problem book in differential geometry

Question

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?

Petersen's Riemanninan Geometry. – M.B. Jan 22 '13 at 12:54 — M.B., Jan 22 '13 at 12:54
Related to my answer here – Yuri Vyatkin Jan 22 '13 at 21:20 — Yuri Vyatkin, Jan 22 '13 at 21:20

score 11 · Answer 1 · answered Sep 08 '17 at 05:14

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.

score 9 · Answer 2 · answered Apr 09 '17 at 05:16

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.

score 8 · Accepted Answer · answered Jan 22 '13 at 12:49

8

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

answered Jan 22 '13 at 12:49

Michael Albanese

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Can you suggest one for beginning undergraduates which has some applications to physics? – Manjil P. Saikia Jun 19 '13 at 08:04
I am not aware of such a book. Try this question for potential suggestions. – Michael Albanese Jun 19 '13 at 08:25

Faraad Armwood · Answer 4 · 2017-09-08T03:35:23.557

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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.

edited Sep 08 '17 at 03:35

answered Oct 14 '16 at 19:04

Faraad Armwood

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Ethan Bolker · Answer 5 · 2022-04-06T14:17:30.503

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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

edited Apr 06 '22 at 14:17

answered Oct 14 '16 at 19:08

Ethan Bolker

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Well, after Volume I the exercises peter off pretty seriously. – Ted Shifrin Apr 09 '17 at 05:21
Link is dead... – Cheng Apr 06 '22 at 05:45
@Cheng Changed the link thanks. (You could have edited.) – Ethan Bolker Apr 06 '22 at 14:18

score 5 · Answer 6 · answered Sep 08 '17 at 07:26

5

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.

answered Sep 08 '17 at 07:26

MMM

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Good problem book in differential geometry

6 Answers6

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