Lagrangian Curves in Affine Symplectic 4-space
arXiv:1305.3092
Abstract
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.
(04/2013)