2015 Volume 67 Issue 2 Pages 195-246
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 [12] and Part I [14], 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.
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