  Lagrangian curves in 4-space entertain intriguing relationships with second
order deformation of plane curves under the special affine group and null
curves in a 3-dimensional Lorentzian space form. We provide a natural affine
symplectic frame for Lagrangian curves. It allows us to classify Lagrangrian
curves with constant symplectic curvatures, to construct a class of Lagrangian
tori and determine Lagrangian geodesics.
