EINSTEIN-WEYL STRUCTURES ON REAL HYPERSURFACES OF COMPLEX TWO-PLANE GRASSMANNIANS

We study real Hopf hypersurfaces with Einstein-Weyl structures in the complex two-plane Grassmannian G(2)(Cm+2 ), m >= 3. First we prove that a real Hopf hypersurface with a closed Einstein-Weyl structure W = (g, theta) is of type (B) if del(xi)theta = 0, where denotes the Reeb vector field of the hypersurface. Next, for a Hopf hypersurface with non-vanishing geodesic Reeb flow, we prove that there does not exist an Einstein-Weyl structure W = (g, k eta), where k is a non-zero constant and eta is a one-form dual to xi. Finally, it is proved that a real Hopf hypersurface with two closed Einstein-Weyl structures W-+/- = (g, +/-theta) is of type (A) or type (B).