Inhomogeneity of Isoparametric Hypersurfaces of OT-FKM-type in the Pseudo-Sphere
Abstract
We study isoparametric hypersurfaces, whose principal curvatures are all constant, in the pseudo-Riemannian space forms. In this paper, we investigate two topics. Firstly, according to representations of Clifford algebras, we give a construction of Clifford systems of signature $(m, r)$ for any $(m, r)$ explicitly. Secondly, we show that a (connected) isoparametric hypersurface of OT-FKM-type whose focal variety is $M_{+}$ in the pseudo-sphere is inhomogeneous if the signature $(m, r)$ of its Clifford system on $\mathbb{R}^{2l}_{s}$ satisfies $m\equiv 0\pmod{4}$, $r\equiv 0\pmod{2}$ and $l>m$, showing that each connected component of $M_{+}$ is inhomogeneous.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2023
- DOI:
- 10.48550/arXiv.2308.13025
- arXiv:
- arXiv:2308.13025
- Bibcode:
- 2023arXiv230813025S
- Keywords:
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- Mathematics - Differential Geometry;
- 53C50;
- 53C30