Hopf hypersurfaces in complex projective space and half-dimensional totally complex submanifolds in complex 2-plane Grassmannian I

We define Gauss map from a real hypersurface in complex projective space to complex 2-plane Grassmannian. We show that if a real hypersurface is Hopf, then the image of the Gauss map is a half-dimensional totally complex submanifold with respect to quaternionic Kähler structure of complex 2-plane Grassmannian.