On Affine Hypersurfaces with an Almost Symplectic Structure

Abstract

In this paper we study affine hypersurfaces additionally equipped with an almost symplectic structure \({\omega}\). In particular we give some conditions for induced connection \({\nabla}\) to be flat or symplectic. Also, we study properties of affine hypersurfaces for which there exists almost symplectic structure \({\omega}\) satisfying condition \({R^{k} \cdot \omega=0}\) and, in particular, hypersurfaces with the property \({\nabla^{k}\omega=0}\).