Abstract

The differential system for minimal Lagrangian surfaces in a 2 C -dimensional, non-flat, complex space form is an elliptic integrable system defined on the Grassmann bundle of oriented Lagrangian 2-planes. This is a 6-symmetric space associated with the Lie group SL ( 3 , C ) , and the minimal Lagrangian surfaces arise as the primitive maps. Utilizing this property, we derive the inductive differential algebraic formulas for a pair of the formal loop algebra s l ( 3 , C ) [ [ λ ] ] -valued canonical formal Killing fields. For applications, (a) we give a complete classification of the (pseudo) Jacobi fields for the minimal Lagrangian system, (b) we obtain an infinite sequence of conservation laws from the components of the canonical formal Killing fields.

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