arXiv subjects

Yuta Sasahara

Publications and source records attributed to Yuta Sasahara.

2 recordsLinked to original sources

arXiv2024

4-Dimensional Isoparametric Hypersurfaces of Index 2 in the Pseudo-Riemannian Space Forms

We study isoparametric hypersurfaces, whose principal curvatures are all constant, in the pseudo-Riemannian space forms. In this paper, we investigate three topics.Firstly, according to Petrov's classification theorem, we give a classification of hypersurfaces of index 2 with respect to a pair of a shape operator and a metric. Therefore, we can define types of isoparametric hypersurfaces of index 2 concerning the classification. Secondly, we give several examples of certain types. Thirdly, we show that there exist no isoparametric hypersurfaces of index 2 whose shape operators have complex principal curvatures in certain cases.

math.DG↗

arXiv2023

Inhomogeneity of Isoparametric Hypersurfaces of OT-FKM-type in the Pseudo-Sphere

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.

math.DG↗