On affine hypersurfaces with an almost symplectic structure (Q511835)

The author studies affine hypersurfaces which also admit a symplectic form \(\omega\) and for which the tensor \(J_{\omega}\) is related to the second fundamental form by \(\omega(X,J_{\omega}Y)=h(X,Y)\). He then investigates when the structure \(J_\omega\) is parallel with respect to the induced connection, thus generalising previous results of Kon for hypersurfaces in the Euclidean space. He also investigates when the symplectic structure is \(k\)-parallel with respect to the induced connection.