Tohoku Mathematical Journal

A Cartan type identity for isoparametric hypersurfaces in symmetric spaces

Naoyuki Koike

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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.

Article information

Tohoku Math. J. (2), Volume 66, Number 3 (2014), 435-454.

First available in Project Euclid: 8 October 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C35: Symmetric spaces [See also 32M15, 57T15]

Isoparametric hypersurface principal curvature focal radius complex focal radius Hermann action


Koike, Naoyuki. A Cartan type identity for isoparametric hypersurfaces in symmetric spaces. Tohoku Math. J. (2) 66 (2014), no. 3, 435--454. doi:10.2748/tmj/1412783206.

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