Books on differential geometry on Banach Spaces.

AI Thread Summary
The discussion centers on recommendations for books and preprints related to the study of Banach manifolds and differential geometry (DG) in a broader context. Participants suggest "The Convenient Setting for Global Analysis," which focuses on infinite-dimensional manifolds, as a valuable resource. There is a consensus on the need for textbooks that cover more general geometric objects beyond standard courses in differential geometry, with Banach manifolds being a key area of interest. Additional recommendations include Lang's "Fundamentals of Differential Geometry" and Abraham, Marsden, and Ratiu's "Manifolds, Tensor Analysis and Applications," which are noted for their comprehensive treatment of the subject. The conversation reflects a quest for deeper understanding and resources in advanced geometric studies.
MathematicalPhysicist
Science Advisor
Gold Member
Messages
4,662
Reaction score
372
Can you recommend me of books or preprints that cover reasonabely well this topic?

Thanks.
 
Physics news on Phys.org
Do you mean the basic study of Banach manifolds h(ttp://en.wikipedia.org/wiki/Banach_manifold)?

In any case, it cannot hurt for you to take a look at the book (free online) "The convenient setting for global analysis" which is a book about infinite dimensional manifolds.
 
Basically I am looking for DG on a more general setting than the one covered in any first course in DG, I guess Hilbert spaces and banach spaces comes next after the real space.

I'll check the book.
 
Well, I now find myself in similar circumstances. I want a textbook on the most general geometric objects possible, but I don't know how much more general you can get then Banach manifolds. I guess the algebraic stuff?
 
Lang's "Fundamentals of Differential Geometry"

And Abraham/Marsden/Ratiu's "Manifolds, Tensor Analysis and applications"
 

Thread 'Opinions/personal experiences on the following four CompSci books'

For the following four books, has anyone used them in a course or for self study? Compiler Construction Principles and Practice 1st Edition by Kenneth C Louden Programming Languages Principles and Practices 3rd Edition by Kenneth C Louden, and Kenneth A Lambert Programming Languages 2nd Edition by Allen B Tucker, Robert E Noonan Concepts of Programming Languages 9th Edition by Robert W Sebesta If yes to either, can you share your opinions about your personal experience using them. I...
View full post »

Thread 'Ashcroft and Mermin: revised edition'

Hi, I have notice that Ashcroft, Mermin and Wei worked at a revised edition of the original solid state physics book (here). The book, however, seems to be never available. I have also read that the reason is related to some disputes related to copyright. Do you have any further information about it? Did you have the opportunity to get your hands on this revised edition? I am really curious about it, also considering that I am planning to buy the book in the near future... Thanks!
View full post »

Similar threads

Differential geometry of singular spaces
Replies
0
Views
2K
Suggestions for HS geometry book (proofs)
Replies
14
Views
1K
Geometry Confusion about Differential Geometry Books
Replies
11
Views
3K
Geometry Geometrical books (differential geometry, tensors, variational mech.)
Replies
2
Views
2K
Geometry Differential Geometry: Book on its applications?
Replies
14
Views
4K
Any other books like David Acheson's "The Wonder Book of Geometry"?
Replies
3
Views
2K
Classical Source recommendation on Differential Geometry
Replies
6
Views
3K
Geometry Recommendation for High School Geometry book
Replies
7
Views
5K
Geometry Classical and modern differential geometry
Replies
9
Views
4K
Geometry Book Recommendations in Differential Geometry
Replies
19
Views
4K

Hot Threads

Recent Insights

Back
Top