PMCV hypersurfaces in non-flat pseudo-Riemannian space forms
Differential Geometry
2024-03-14 v1
Abstract
In this paper, we prove that PMCV (i.e. \Delta\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.
Cite
@article{arxiv.2403.08205,
title = {PMCV hypersurfaces in non-flat pseudo-Riemannian space forms},
author = {Chao Yang and Jiancheng Liu and Li Du},
journal= {arXiv preprint arXiv:2403.08205},
year = {2024}
}