Some differential-geometric properties of $R$-spaces

Song, Hyunjung

doi:10.21099/tkbjm/1496164288

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Cited by 3 publications

References 24 publications

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Moment Maps and Isoparametric Hypersurfaces in Spheres — Hermitian Cases

Fujii

Tamaru

2015

Transformation Groups

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We are studying 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 squared-norms of the moment maps for some Hamiltonian actions. The proof is based on the structure theory of symmetric spaces.

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Moment Maps and Isoparametric Hypersurfaces in Spheres — Hermitian Cases

Fujii

Tamaru

2015

Transformation Groups

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Lie-algebraic characterization of tangentially degenerate orbits of s-representations

Ikawa¹,

Sakai²,

Tasaki³

2010

Differential Geometry and its Applications

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Parallel Kähler submanifolds and 𝑅-spaces

Ohnita¹

2022

Contemporary Mathematics

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Parallel Kähler submanifolds here mean complex submanifolds immersed in complex projective spaces with parallel second fundamental form. The classification of such submanifolds was done first by Hisao Nakagawa and Ryoichi Takagi (1976) and reproduced secondly and thirdly by Masaru Takeuchi (1978, 1984) by two different methods of unitary representation theory and Jordan triple systems. In this article we briefly survey such related submanifold theory and give the fourth proof for the classification theorem by a different approach based on the differential geometric characterization of R R -spaces due to Carlos Olmos and Cristián U. Sánchez (1991).

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Some differential-geometric properties of $R$-spaces

Cited by 3 publications

References 24 publications

Moment Maps and Isoparametric Hypersurfaces in Spheres — Hermitian Cases

Moment Maps and Isoparametric Hypersurfaces in Spheres — Hermitian Cases

Lie-algebraic characterization of tangentially degenerate orbits of s-representations

Parallel Kähler submanifolds and 𝑅-spaces

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