Four dimensional hypersurfaces with proper mean curvature vector field in pseudo-Riemannian space forms
Differential Geometry
2023-03-07 v1
Abstract
In this paper, we study four dimensional hypersurface M^4_r with proper mean curvature vector field (i.e. \Delta\vec{H} is proportional to \vec{H}) in pseudo-Riemannian space form N^5_s(c), and show that it has constant mean curvature, and give the range of this constant. As an application, we get that biharmonic hypersurfaces in N^5_s(c) are minimal in some specific cases, which partially confirms B.-Y. Chen's conjecture.
Keywords
Cite
@article{arxiv.2303.02362,
title = {Four dimensional hypersurfaces with proper mean curvature vector field in pseudo-Riemannian space forms},
author = {Chao Yang and Jiancheng Liu and Li Du},
journal= {arXiv preprint arXiv:2303.02362},
year = {2023}
}