In this paper we determine the Hamiltonian stability of Gauss images, i.e., the images of the Gauss maps, of homogeneous isoparametric hypersurfaces of exceptional type with $g=6$ or $4$ distinct principal curvatures in spheres. Combining it with our previous results in  and Part I , we determine the Hamiltonian stability for the Gauss images of all homogeneous isoparametric hypersurfaces. In addition, we discuss the exceptional Riemannian symmetric space $(E_6, U(1)\cdot Spin(10))$ and the corresponding Gauss image, which have their own interest from the viewpoint of symmetric space theory.
"Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces II." Tohoku Math. J. (2) 67 (2) 195 - 246, 2015. https://doi.org/10.2748/tmj/1435237041