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.
Citation
Naoyuki Koike. "A Cartan type identity for isoparametric hypersurfaces in symmetric spaces." Tohoku Math. J. (2) 66 (3) 435 - 454, 2014. https://doi.org/10.2748/tmj/1412783206
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