U(1)-invariant special Lagrangian 3-folds. I. nonsingular solutions

This is the first of three papers studying special Lagrangian 3-submanifolds (SL 3-folds) N in ℂ3 invariant under the U(1)-action eiθ:(z1,z2, z3) (eiθz1, e-iθz2,z3), using analytic methods. Let N be such a U(1)-invariant SL 3-fold. Then z12- z22=2a on N for some a∈ℝ. Locally, N can be written as a k...