We consider curves in ℝ2n endowed with the standard symplectic structure. We introduce the concept of symplectic arc length for curves. We construct an adapted symplectic Frenet frame and we define 2n - 1 local differential invariants that we call symplectic curvatures of the curve. We prove that up to a rigid symplectic motion of ℝ2n, there exists a unique curve with prescribed symplectic curvatures. We characterize the curves in ℝ4 with constant symplectic curvatures.
Bibliographical noteFunding Information:
The research of the first author was supported in part by NSERC grant RGPIN 105490-2004, the second author by NSF Grant DMS 05-05293, and the third author by CNPq Grant 306117/2006-1.
- Moving frames
- Symplectic curvatures
- Symplectic curves