Books on differential geometry on Banach Spaces.

Click For Summary

Discussion Overview

The discussion revolves around recommendations for books or preprints on differential geometry specifically related to Banach spaces and Banach manifolds. Participants express interest in resources that cover the topic beyond introductory courses in differential geometry.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant requests recommendations for books or preprints on differential geometry in the context of Banach spaces.
  • Another participant suggests looking into the concept of Banach manifolds and recommends "The convenient setting for global analysis," which addresses infinite dimensional manifolds.
  • A participant expresses a desire for resources that cover differential geometry in a more general context than typical introductory courses, specifically mentioning Hilbert and Banach spaces.
  • Another participant shares a similar interest in finding a textbook on the most general geometric objects, questioning how much more general one can get than Banach manifolds.
  • A participant references a related question that appeared on MathOverflow regarding books on Banach manifolds.
  • Two specific textbooks are recommended: Lang's "Fundamentals of Differential Geometry" and Abraham/Marsden/Ratiu's "Manifolds, Tensor Analysis and applications."

Areas of Agreement / Disagreement

Participants express varying interests in the scope of differential geometry related to Banach spaces, with no consensus on a single recommended resource or approach. Multiple viewpoints on the generality of the subject matter are presented.

Contextual Notes

Participants do not clarify the specific prerequisites or foundational knowledge required for the suggested resources, nor do they resolve the extent to which Banach manifolds encompass the general geometric objects of interest.

Who May Find This Useful

Readers interested in advanced topics in differential geometry, particularly in the context of functional analysis and infinite dimensional spaces, may find this discussion relevant.

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"
 

Similar threads

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