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The submanifold geometries associated to Grassmannian systems

About this Title

Martina Brück, Xi Du, Joonsang Park and Chuu-Lian Terng

Publication: Memoirs of the American Mathematical Society
Publication Year: 2002; Volume 155, Number 735
ISBNs: 978-0-8218-2753-6 (print); 978-1-4704-0328-7 (online)
DOI: https://doi.org/10.1090/memo/0735
MathSciNet review: 1875645
MSC: Primary 53C40; Secondary 35A30, 35Q53, 35Q55, 37K25, 53C42

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Table of Contents

Chapters

  • 1. Introduction
  • 2. The $U/K$-system
  • 3. $G_{m,n}$-systems
  • 4. $G^1_{m,n}$-systems
  • 5. Moving frame method for submanifolds
  • 6. Submanifolds associated to $G_{m,n}$-systems
  • 7. Submanifolds associated to $G^1_{m,n}$-systems
  • 8. $G^1_m,1$-systems and isothermic surfaces
  • 9. Loop group action for $G_{m,n}$-systems
  • 10. Ribaucour transformations for $G_{m,n}$-systems
  • 11. Loop group actions for $G^1_{m,n}$-systems
  • 12. Ribaucour transformations for $G^1_{m,n}$-systems
  • 13. Darboux transformations for $G^1_{m,n}$-systems
  • 14. Bäcklund transformations and loop group factorizations
  • 15. Permutability formula for Ribaucour transformations
  • 16. The $U/K$-hierarchy and finite type solutions