Books on differential geometry on Banach Spaces.

Banach manifolds. In summary, there are several books available for studying Banach manifolds, including "The convenient setting for global analysis" and "Fundamentals of Differential Geometry" by Lang. Another good resource is "Manifolds, Tensor Analysis and Applications" by Abraham, Marsden, and Ratiu. These books cover the basic study of Banach manifolds and also provide information on more general geometric objects.
  • #1
MathematicalPhysicist
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Can you recommend me of books or preprints that cover reasonabely well this topic?

Thanks.
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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?
 
  • #6
Lang's "Fundamentals of Differential Geometry"

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

1. What is differential geometry on Banach spaces?

Differential geometry on Banach spaces is a branch of mathematics that studies the properties and structures of smooth spaces, such as curves and surfaces, that are defined on Banach spaces. It combines concepts from differential geometry and functional analysis to study the geometric properties of these spaces.

2. What are some common topics covered in books on differential geometry on Banach spaces?

Some common topics covered in books on differential geometry on Banach spaces include smooth mappings, tangent spaces, curvature, geodesics, and Riemannian metrics. Other topics may include applications of differential geometry on Banach spaces in physics, engineering, and other fields.

3. Who can benefit from studying books on differential geometry on Banach spaces?

Books on differential geometry on Banach spaces can be beneficial for mathematicians, physicists, engineers, and other professionals who are interested in understanding complex geometric structures and their applications. It can also be useful for graduate students and researchers in these fields.

4. Are there any prerequisites for studying books on differential geometry on Banach spaces?

A solid understanding of basic concepts in differential geometry and functional analysis is necessary for studying books on differential geometry on Banach spaces. Knowledge of topology, linear algebra, and calculus is also helpful.

5. Can differential geometry on Banach spaces be applied to other fields?

Yes, differential geometry on Banach spaces has many applications in physics, engineering, and other fields. It can be used to study the behavior of physical systems, such as fluid dynamics and general relativity, and to develop efficient algorithms for optimization problems in engineering and computer science.

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