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arXiv · 2403.11165

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

Yuta Sasahara
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Abstract

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.

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BibTeXRIS

Yuta Sasahara. 2024-03-17. 4-Dimensional Isoparametric Hypersurfaces of Index 2 in the Pseudo-Riemannian Space Forms. https://arxiv.org/abs/2403.11165

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