A Cartan type identity for isoparametric hypersurfaces in symmetric spaces
Differential Geometry
2014-09-22 v4
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.
Keywords
Cite
@article{arxiv.1010.1652,
title = {A Cartan type identity for isoparametric hypersurfaces in symmetric spaces},
author = {Naoyuki Koike},
journal= {arXiv preprint arXiv:1010.1652},
year = {2014}
}
Comments
20pages