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The Submanifold Geometries Associated to Grassmannian Systems
Martina Brück and Xi Du, Joonsang Park, Dongguk University, Seoul, Korea, and Chuu-Lian Terng, Northeastern University, Boston, MA

Memoirs of the American Mathematical Society
2002; 95 pp; softcover
Volume: 155
ISBN-10: 0-8218-2753-7
ISBN-13: 978-0-8218-2753-6
List Price: US$59
Individual Members: US$35.40
Institutional Members: US$47.20
Order Code: MEMO/155/735
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Graduate students and research mathematicians interested in differential geometry and partial differential equations.

Table of Contents

  • Introduction
  • The \(U/K\)-system
  • \(G_{m,n}\)-systems
  • \(G_{m,n}^1\)-systems
  • Moving frame method for submanifolds
  • Submanifolds associated to \(G_{m,n}\)-systems
  • Submanifolds associated to \(G_{m,n}^1\)-systems
  • \(G_{m,1}^1\)-systems and isothermic surfaces
  • Loop group action for \(G_{m,n}\)-systems
  • Ribaucour transformations for \(G_{m,n}\)-systems
  • Loop group action for \(G_{m,n}^1\)-systems
  • Ribaucour transformations for \(G_{m,n}^1\)-systems
  • Darboux transformations for \(G_{m,1}^1\)-systems
  • Bäcklund transformations and loop group factorizations
  • Permutability formula for ribaucour transformations
  • The \(U/K\)-hierarchy and finite type solutions
  • Pictures
  • Bibliography
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