Abstract
We study 3-dimensional minimal Lagrangian submanifolds of the 3-dimensional complex projective space ℂP3 (4) which admit a unit length Killing vector field whose integral curves are geodesics. We show that such Lagrangian submanifolds can be obtained from either horizontal holomorphic curves in ℝP3 (4) (or equivalently superminimal immersions of surfaces in S4 (1)) or from solutions of the two dimensional sinh-Gordon equation. In the latter case, we explicitly obtain the immersions in terms of elliptic functions in the case that the solutions of the sinh-Gordon equation depend only on one variable.
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