Tohoku Mathematical Journal 2015 June SECOND SERIES VOL. 67, NO. 2

 Tohoku Math. J. 67 (2015), 195-246

Title HAMILTONIAN STABILITY OF THE GAUSS IMAGES OF HOMOGENEOUS ISOPARAMETRIC HYPERSURFACES II

Author Hui Ma and Yoshihiro Ohnita

(Received November 1, 2013, revised March 6, 2014)
Abstract. 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.

Mathematics Subject Classification. Primary 53C42; Secondary 53C40, 53D12.

Key words and phrases. Lagrangian submanifold, minimal submanifold, Hamiltonian stability, Gauss map, isoparametric hypersurface.