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Elliptic Integrable Systems: A Comprehensive Geometric Interpretation
 
Idrisse Khemar Université Henri Poincaré, Vandoeuvre-lès-Nancy, France
Elliptic Integrable Systems: A Comprehensive Geometric Interpretation
eBook ISBN:  978-0-8218-9114-8
Product Code:  MEMO/219/1031.E
List Price: $88.00
MAA Member Price: $79.20
AMS Member Price: $52.80
Elliptic Integrable Systems: A Comprehensive Geometric Interpretation
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Elliptic Integrable Systems: A Comprehensive Geometric Interpretation
Idrisse Khemar Université Henri Poincaré, Vandoeuvre-lès-Nancy, France
eBook ISBN:  978-0-8218-9114-8
Product Code:  MEMO/219/1031.E
List Price: $88.00
MAA Member Price: $79.20
AMS Member Price: $52.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2192012; 217 pp
    MSC: Primary 53;

    In this paper, the author studies all the elliptic integrable systems, in the sense of C, that is to say, the family of all the \(m\)-th elliptic integrable systems associated to a \(k^\prime\)-symmetric space \(N=G/G_0\). The author describes the geometry behind this family of integrable systems for which we know how to construct (at least locally) all the solutions. The introduction gives an overview of all the main results, as well as some related subjects and works, and some additional motivations.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Notation, conventions and general definitions
    • 1. Invariant connections on reductive homogeneous spaces
    • 2. $m$-th elliptic integrable system associated to a $k’$-symmetric space
    • 3. Finite order isometries and twistor spaces
    • 4. Vertically harmonic maps and harmonic sections of submersions
    • 5. Generalized harmonic maps
    • 6. Generalized harmonic maps into $f$-manifolds
    • 7. Generalized harmonic maps into reductive homogeneous spaces
    • 8. Appendix
    • List of symbols
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2192012; 217 pp
MSC: Primary 53;

In this paper, the author studies all the elliptic integrable systems, in the sense of C, that is to say, the family of all the \(m\)-th elliptic integrable systems associated to a \(k^\prime\)-symmetric space \(N=G/G_0\). The author describes the geometry behind this family of integrable systems for which we know how to construct (at least locally) all the solutions. The introduction gives an overview of all the main results, as well as some related subjects and works, and some additional motivations.

  • Chapters
  • Introduction
  • Notation, conventions and general definitions
  • 1. Invariant connections on reductive homogeneous spaces
  • 2. $m$-th elliptic integrable system associated to a $k’$-symmetric space
  • 3. Finite order isometries and twistor spaces
  • 4. Vertically harmonic maps and harmonic sections of submersions
  • 5. Generalized harmonic maps
  • 6. Generalized harmonic maps into $f$-manifolds
  • 7. Generalized harmonic maps into reductive homogeneous spaces
  • 8. Appendix
  • List of symbols
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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