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June 2014 Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces, I
Hui Ma, Yoshihiro Ohnita
J. Differential Geom. 97(2): 275-348 (June 2014). DOI: 10.4310/jdg/1405447807

Abstract

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 $Q_n(\mathrm{C})$. 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 On Lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres and Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces II, we completely determine the Hamiltonian stability of the Gauss images of all homogeneous isoparametric hypersurfaces.

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Hui Ma. Yoshihiro Ohnita. "Hamiltonian stability of the Gauss images of homogeneous isoparametric hypersurfaces, I." J. Differential Geom. 97 (2) 275 - 348, June 2014. https://doi.org/10.4310/jdg/1405447807

Information

Published: June 2014
First available in Project Euclid: 15 July 2014

zbMATH: 1306.53053
MathSciNet: MR3263508
Digital Object Identifier: 10.4310/jdg/1405447807

Rights: Copyright © 2014 Lehigh University

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Vol.97 • No. 2 • June 2014
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