The complex two-plane Grassmannian G(2)(Cm+2) carries a Kahler structure J and also a quaternionic Kahler structure J. For m greater than or equal to 3 we consider the classes of connected real hypersurfaces (M, g) with normal bundle M-perpendicular to such that J(M-perpendicular to) and J(M-perpendicular to) are invariant under the action of the shape operator. We prove that the corresponding unit Hopf vector herds on these hypersurfaces always define minimal immersions of (M, g), and harmonic maps from (M,g), into the unit tangent sphere bundle (T1M,g(s)) with Sasaki metric gs. The radial unit vector fields corresponding to the tubular hypersurfaces are also minimal and harmonic. Similar results hold for the dual space G(2)(Cm+2)*. 1991 Mathematics Subject Classification: 53C20, 53C25, 53C35, 53C40, 53C42, 53C55, 58E20.