Integrable systems and invariant curve flows in centro-equiaffine symplectic geometry

In this paper, the theory for curves in centro-equiaffine symplectic geometry is established. Integrable systems satisfied by the curvatures of curves under inextensible motions in centro-equiaffine symplectic geometry are identified. It is shown that certain non-stretching invariant curve flows in centro-equiaffine symplectic geometry are closely related to the matrix KdV equations and their extension.

► Established the theory for curves in centro-equiaffine symplectic geometry.
► Integrable systems for inextensible motions in the geometry are identified.
► Obtained matrix KdV equations and their extension from the invariant curve flows.