2024/03/17 by Yuta Sasahara, Sasahara, Yuta
Mathematics · Physics and Astronomy · #53B30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2403.11165
openalex publication_date 2024/03/17 · openalex created_date 2024/03/20 · openalex updated_date 2026/07/28
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.