What Are the Best Books on Differential Geometry with Proofs and Exercises?

[WittyName]

As the title says. Can anyone recommend me some good books for differential geometry(preferably ones with proofs and examples/exercises)?

 

[jedishrfu]

https://www.amazon.com/dp/0486667219/?tag=pfamazon01-20

or take your pic:



and an ebook to get started right away:

http://samizdat.mines.edu/difgeom/Shr3b.pdf

 

[micromass]

As the title says. Can anyone recommend me some good books for differential geometry(preferably ones with proofs and examples/exercises)?

What level should the books be?? Undergrad, grad? Do you know topology, analysis, linear algebra,...??

 

[WittyName]

https://www.amazon.com/dp/0486667219/?tag=pfamazon01-20

or take your pic:



and an ebook to get started right away:

http://samizdat.mines.edu/difgeom/Shr3b.pdf

Thanks i'll be sure to check them out.

What level should the books be?? Undergrad, grad? Do you know topology, analysis, linear algebra,...??

It's an undergrad course but i want to do some preliminary reading. Yes to both analysis and linear algebra, but no to topology.

 

[micromass]

It's an undergrad course but i want to do some preliminary reading. Yes to both analysis and linear algebra, but no to topology.

You can't go wrong with these two books:

https://www.amazon.com/dp/0132641437/?tag=pfamazon01-20

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

 

[WittyName]

You can't go wrong with these two books:

https://www.amazon.com/dp/0132641437/?tag=pfamazon01-20

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

Much appreciated :D

 

[Daverz]

I have this one on my iPad, and it's very good:

http://www.math.uga.edu/%7Eshifrin/ShifrinDiffGeo.pdf

(from http://www.math.uga.edu/~shifrin/)

 

[A. Bahat]

I also like do Carmo for the basic curves and surfaces stuff. Once you learn a little topology (not much) you should check out Spivak (especially Volumes 1 and 2). Spivak's differential geometry books are awesome.

 

[CJ2116]

The book by Do Carmo was pretty good. I used it as a supplement in my differential geometry course in college, although it was a little bit advanced for me because it was the first time that I had ever seen any of the material.

A great introductory book is Barrett O'Neil's Elementary Differential Geometry. It has a lot of worked problems and solutions in the back so you can check yourself.

For more problems, try the Schaum's Outline of Differential Geometry

There isn't a perfect overlap of content and notation between these books, but I found that it was more than enough to do well in differential geometry. One thing to remember (which I learned the hard way!) is that 80% of the difficulty is understanding notation! So, the more resources, the better.

 

[coalquay404]

If you're coming at this from a physicist's point of view, both Nakahara's and Chris Isham's books on differential geometry are great. (Google is your friend, etc.)