Introduction book to Differential Geometry

[Jianphys17]

Hello everyone, I've 2 books on manifolds theory in e-form:
1) Spivack, calculus on manifold
2) Munkres, analysis on manifold
What would be good to begin with?
Thank you in advance

 

[micromass]

1) Neither of those covers differential geometry. They only cover calc III made rigorous.
2) You need to give us way more information about you, your background, your goals, your (dis)likes,etc. if you want a good anwer.

 

[jedishrfu]

While you ponder Micromass' question the wikipedia article on differential geometry has several books listed at the end:

https://en.wikipedia.org/wiki/Differential_geometry

 

[Jianphys17]

No, I'm apologize the post title was wrong . I meant the diff manifold book, which is better?

 

[The Bill]

Munkres is a bit easier, and the exercises in Spivak are better.

If you own both, I'd recommend working through Spivak, and reading the parallel sections in Munkres when you need more explanation.

 

[malawi_glenn]

I have not studied it from front to cover and have nothing to compare with but Lee - introduction to smooth manifolds is considered to be a gem

 

[Jianphys17]

I have not studied it from front to cover and have nothing to compare with but Lee - introduction to smooth manifolds is considered to be a gem

Yes but Lee's book isn't more for pure mathematicians, than physicist ?

 

[micromass]

Yes but Lee's book isn't more for pure mathematicians, than physicist ?

How are we supposed to give you suitable recommendations if you ignore our posts and tell us nothing about you, your background, your goals, your (dis)likes,etc.

 

[George Jones]

Yes but Lee's book isn't more for pure mathematicians, than physicist ?

How about Fecko, then? Fecko has lots of examples given as short exercises.

Another book worth looking at is Differential Geometry and Lie Groups for Physicists by Marian Fecko,
https://www.amazon.com/dp/0521187966/?tag=pfamazon01-20

This book is not as rigorous as the books by Lee and Tu, but it more rigorous and comprehensive than the book by Schutz. Fecko treats linear connections and associated curvature, and connections and curvature for bundles. Consequently, Fecko can be used for a more in-depth treatment of the math underlying both GR and gauge field theories than traditionally is presented in physics courses.

Fecko has an unusual format. From its Preface,

A specific feature of this book is its strong emphasis on developing the general theory through a large number of simple exercises (more than a thousand of them), in which the reader analyzes "in a hands-on fashion" various details of a "theory" as well as plenty of concrete examples (the proof of the pudding is in the eating).

The book is reviewed at the Canadian Association of Physicists website,

http://www.cap.ca/BRMS/Reviews/Rev857_554.pdf.

From the review

There are no problems at the end of each chapter, but that's because by the time you reached the end of the chapter, you feel like you've done your homework already, proving or solving every little numbered exercise, of which there can be between one and half a dozen per page. Fortunately, each chapter ends with a summary and a list of relevant equations, with references back to the text. ...

A somewhat idiosyncratic flavour of this text is reflected in the numbering: there are no numbered equations, it's the exercises that are numbered, and referred to later.

Personal observations based on my limited experience with my copy of the book:

1) often very clear, but sometimes a bit unclear;
2) some examples of mathematical imprecision/looseness, but these examples are not more densely distributed than in, say, Nakahara;
3) the simple examples are often effective.

 

[malawi_glenn]

If I remember correctly, Spivak require pretty much background knowledge of the subject.

 

[Jianphys17]

How are we supposed to give you suitable recommendations if you ignore our posts and tell us nothing about you, your background, your goals, your (dis)likes,etc.

My current math background includes analysis 1,2 and general topology!

 

[malawi_glenn]

and your goal is physics?

 

[Jianphys17]

and your goal is physics?

Yes , sorry i should have put it, i forgot write it up!