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PMCV hypersurfaces in non-flat pseudo-Riemannian space forms

Chao Yang, Jiancheng Liu, Li Du

Abstract

In this paper, we prove that PMCV (i.e. Δ\vec{H} is proportional to \vec{H}) hypersurface M^n_r of a non-flat pseudo-Riemannian space form N^{n+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.

PMCV hypersurfaces in non-flat pseudo-Riemannian space forms

Abstract

In this paper, we prove that PMCV (i.e. Δ\vec{H} is proportional to \vec{H}) hypersurface M^n_r of a non-flat pseudo-Riemannian space form N^{n+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.
Paper Structure (4 sections, 64 equations)

This paper contains 4 sections, 64 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. PMCV hypersurfaces in non-flat pseudo-Riemannian space forms
  4. Classification of non-minimal Lorentzian PMCV hypersurfaces in $\mathbb{H}^{n+1}_1$ and $\mathbb{S}^{n+1}_1$