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Books on differential geometry on Banach Spaces.

  1. Jul 25, 2011 #1

    MathematicalPhysicist

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    Can you recommend me of books or preprints that cover reasonabely well this topic?

    Thanks.
     
  2. jcsd
  3. Jul 25, 2011 #2

    quasar987

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    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.
     
  4. Jul 25, 2011 #3

    MathematicalPhysicist

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    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.
     
  5. Apr 28, 2012 #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. Apr 28, 2012 #5

    mathwonk

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  7. Apr 28, 2012 #6
    Lang's "Fundamentals of Differential Geometry"

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