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MOMENT MAPS AND ISOPARAMETRIC HYPERSURFACES IN SPHERES — HERMITIAN CASES

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Abstract

We study a relationship between isoparametric hypersurfaces in spheres with four distinct principal curvatures and the moment maps of certain Hamiltonian actions. In this paper, we consider the isoparametric hypersurfaces obtained from the isotropy representations of compact irreducible Hermitian symmetric spaces of rank two. We prove that the Cartan-Münzner polynomials of these hypersurfaces can be written as squarednorms of the moment maps for some Hamiltonian actions. The proof is based on the structure theory of symmetric spaces.

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Authors and Affiliations

  1. General Education Division, National Institute of Technology Oshima College, 1091-1 Komatsu, SuouOshima-cho, Oshima-gun, Yamaguchi, 742-2193, Japan

    SHINOBU FUJII

  2. Department of Mathematics, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526, Japan

    HIROSHI TAMARU

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  1. SHINOBU FUJII
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  2. HIROSHI TAMARU
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Correspondence to SHINOBU FUJII.

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FUJII, S., TAMARU, H. MOMENT MAPS AND ISOPARAMETRIC HYPERSURFACES IN SPHERES — HERMITIAN CASES. Transformation Groups 20, 417–436 (2015). https://doi.org/10.1007/s00031-015-9305-1

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