Semi-parallel and parallel symplectic surfaces in the four-dimensional symplectic space

Abstract

Parallel and semi-parallel symplectic surfaces in the symplectic space Sp₄ are studied. It is proved that a symplectic surface is semi-parallel if and only if its tangent connection is flat. The parallel symplectic surfaces are characterized and the existence of semi-parallel symplectic surfaces which are not parallel is exhibited. The study is conducted by the method of moving frame.