The Characterization of Affine Symplectic Curves in ℝ⁴

Abstract

Symplectic geometry arises as the natural geometry of phase-space in the equations of classical mechanics. In this study, we obtain new characterizations of regular symplectic curves with respect to the Frenet frame in four-dimensional symplectic space. We also give the characterizations of the symplectic circular helices as the third- and fourth-order differential equations involving the symplectic curvatures.

Keywords

• symplectic curves
• circular helices
• symplectic curvatures
• Frenet frame