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HOME > Table of Contents and Abstracts > Vol. 67, No. 2
Tohoku Mathematical Journal
2015
June
SECOND SERIES VOL. 67, NO. 2
Tohoku Math. J.
67 (2015), 195-246
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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.
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