A Cartan type identity for isoparametric hypersurfaces in symmetric spaces

Naoyuki Koike

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arXiv · 1010.1652

A Cartan type identity for isoparametric hypersurfaces in symmetric spaces

Naoyuki Koike

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Abstract

In this paper, we obtain a Cartan type identity for curvature-adapted isoparametric hypersurfaces in symmetric spaces of compact type or non-compact type. This identity is a generalization of Cartan-D'Atri's identity for curvature-adapted(=amenable) isoparametric hypersurfaces in rank one symmetric spaces. Furthermore, by using the Cartan type identity, we show that certain kind of curvature-adapted isoparametric hypersurfaces in a symmetric space of non-compact type are principal orbits of Hermann actions.

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Naoyuki Koike. 2010-10-08. A Cartan type identity for isoparametric hypersurfaces in symmetric spaces. https://arxiv.org/abs/1010.1652

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