Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces I

Hui Ma Tsinghua University, Beijing Yoshihiro Ohnita Osaka City University, Japan

Differential Geometry mathscidoc:1705.10001

Distinguished Paper Award in 2017

Journal of Differential Geometry, 97, 275-348, 2014
The image of the Gauss map of any oriented isoparametric hypersurface in the standard unit sphere $S^{n+1}(1)$ is a minimal Lagrangian submanifold in the complex hyperquadric $Q_n(\mathbb{C})$. In this paper we show that the Gauss image of a compact oriented isoparametric hypersurface with $g$ distinct constant principal curvatures in $S^{n+1}(1)$ is a compact monotone and cyclic embedded Lagrangian submanifold with minimal Maslov number $2n/g$. We obtain the Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces of classical type with $g = 4$. Combining with our results in [25] and [27], we completely determine the Hamiltonian stability of the Gauss images of all homogeneous isoparametric hypersurfaces.
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@inproceedings{hui2014hamiltonian,
  title={Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces I},
  author={Hui Ma, and Yoshihiro Ohnita},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170529234559840127754},
  booktitle={Journal of Differential Geometry},
  volume={97},
  pages={275-348},
  year={2014},
}
Hui Ma, and Yoshihiro Ohnita. Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces I. 2014. Vol. 97. In Journal of Differential Geometry. pp.275-348. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170529234559840127754.
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