- #1

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thanks

- Thread starter lee.spi
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- #1

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thanks

- #2

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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/dp/0132125897/?tag=pfamazon01-20&tag=pfamazon01-20

- https://www.amazon.com/dp/184882890X/?tag=pfamazon01-20&tag=pfamazon01-20

- https://www.amazon.com/dp/0521721490/?tag=pfamazon01-20&tag=pfamazon01-20

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/dp/1441979395/?tag=pfamazon01-20&tag=pfamazon01-20

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

https://www.amazon.com/dp/1441999817/?tag=pfamazon01-20&tag=pfamazon01-20

and

https://www.amazon.com/dp/0387983228/?tag=pfamazon01-20&tag=pfamazon01-20

- https://www.amazon.com/dp/0132125897/?tag=pfamazon01-20&tag=pfamazon01-20

- https://www.amazon.com/dp/184882890X/?tag=pfamazon01-20&tag=pfamazon01-20

- https://www.amazon.com/dp/0521721490/?tag=pfamazon01-20&tag=pfamazon01-20

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/dp/1441979395/?tag=pfamazon01-20&tag=pfamazon01-20

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

https://www.amazon.com/dp/1441999817/?tag=pfamazon01-20&tag=pfamazon01-20

and

https://www.amazon.com/dp/0387983228/?tag=pfamazon01-20&tag=pfamazon01-20

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- #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]

I recommend it:

http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf [Broken]

Last edited by a moderator:

- #4

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I already linked that.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:

- #5

mathwonk

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ah yes! now i see it. i am glad you also like that one.

- #6

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i was reading this book , it is a good book , thanks

- #7

- 57

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Here is one with an emphasis on numerical methods of differential geometry (especially Chapter 5) with lots of source codes in C/C++:

thanks

https://www.amazon.com/dp/0646594044/?tag=pfamazon01-20&tag=pfamazon01-20

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- #8

- 53

- 3

William L. Burke: Applied Differential Geometry if you know some physics.

- #9

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Shlomo Sternberg: Curvature in Mathematics and Physics

- #10

- 990

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Not an introductory text. You really need to have some familiarity with differential geometry on manifolds to understand it.Shlomo Sternberg: Curvature in Mathematics and Physics

- #11

- 53

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if you read his Advanced calculus book ,you'll get probably the prerequisites you need for it.Not an introductory text. You really need to have some familiarity with differential geometry on manifolds to understand it.

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