Hypersurfaces with proper mean curvature vector field in non-flat pseudo-Riemannian space forms

Abstract

In this paper, we prove that hypersurface M_rⁿ with proper mean curvature vector field (i.e. Δ is proportional to ) and at most two distinct principal curvatures in a non-flat pseudo-Riemannian space form N_sⁿ⁺¹(c) 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.