Formal Killing fields for minimal Lagrangian surfaces in complex space forms

2013/11/11 by Joe S. Wang, Wang, Joe S.
Mathematics · #35A27 #53C43 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:35A27 #msc:53C43

paper · pdf · doi:10.48550/arxiv.1311.2464

57 pages. v4. misprints are corrected

arxiv created 2014/09/03 · arxiv updated 2014/09/05

Abstract

The differential system for minimal Lagrangian surfaces in a 2_ℂ-dimensional, non-flat, complex space form is an elliptic system defined on the bundle of oriented Lagrangian 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 differential algebraic inductive formulas for a pair of loop algebra \mathfraksl(3,ℂ)[[λ]]-valued canonical formal Killing fields. As a result, we give a complete classification of the (infinite sequence of) Jacobi fields for the minimal Lagrangian system. We also obtain an infinite sequence of higher-order conservation laws from the components of the formal Killing fields.

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