Tohoku Mathematical Journal

Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces II

Hui Ma and Yoshihiro Ohnita

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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.

Article information

Source
Tohoku Math. J. (2), Volume 67, Number 2 (2015), 195-246.

Dates
First available in Project Euclid: 25 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1435237041

Digital Object Identifier
doi:10.2748/tmj/1435237041

Mathematical Reviews number (MathSciNet)
MR3365370

Zentralblatt MATH identifier
1334.53060

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 53C40: Global submanifolds [See also 53B25] 53D12: Lagrangian submanifolds; Maslov index

Keywords
Lagrangian submanifold minimal submanifold Hamiltonian stability Gauss map isoparametric hypersurface

Citation

Ma, Hui; Ohnita, Yoshihiro. Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces II. Tohoku Math. J. (2) 67 (2015), no. 2, 195--246. doi:10.2748/tmj/1435237041. https://projecteuclid.org/euclid.tmj/1435237041


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