Tohoku Mathematical Journal
2010
June
SECOND SERIES VOL. 62, NO. 2

Tohoku Math. J.
62 (2010), 191-213

Title HOMOGENEOUS ISOPARAMETRIC HYPERSURFACES IN SPHERES WITH FOUR DISTINCT PRINCIPAL CURVATURES AND MOMENT MAPS

Author Shinobu Fujii

(Received August 27, 2009, revised December 25, 2009)
Abstract. We study relations between moment maps of Hamiltonian actions and isoparametric hypersurfaces in spheres with four distinct principal curvatures. In this paper, we deal with the isoparametric hypersurfaces given by the isotropy representations of compact irreducible Hermitian symmetric spaces of classical type and of rank two. We show that such isoparametric hypersurfaces can be obtained by moment maps. More precisely, certain squared-norms of moment maps coincide with Cartan-Münzner polynomials, which are defining-equations, of above isoparametric hypersurfaces.

2000 Mathematics Subject Classification. Primary 53A07; Secondary 37J15.
Key words and phrases. Isoparametric hypersurfaces, moment maps.

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