PMCV hypersurfaces in non-flat pseudo-Riemannian space forms

2024/03/13 by Chao Yang, Yang, Chao, Jiancheng Liu +3
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2403.08205

openalex publication_date 2024/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that PMCV (i.e. ΔH is proportional to H) hypersurface Mⁿ_r of a non-flat pseudo-Riemannian space form Nⁿ⁺¹_s(c) with at most two distinct principal curvatures is minimal or locally isoparametric, and compute the mean curvature for the isoparametric ones. As an application, we give full classification results of such non-minimal Lorentzian hypersurfaces of non-flat Lorentz space forms.

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