The Submanifold Geometries Associated to Grassmannian Systems

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 Backlund transformations and loop group factorizations Permutability formula for ribaucour transformations The $U/K$-hierarchy and finite type solutions Pictures Bibliography.