Four dimensional biharmonic hypersurfaces in nonzero space form have constant mean curvature
Differential Geometry
2020-12-02 v1
Abstract
In this paper, through making careful analysis of Gauss and Codazzi equations, we prove that four dimensional biharmonic hypersurfaces in nonzero space form have constant mean curvature. Our result gives the positive answer to the conjecture proposed by Balmus-Montaldo-Oniciuc in 2008 for four dimensional hypersurfaces.
Keywords
Cite
@article{arxiv.2007.13589,
title = {Four dimensional biharmonic hypersurfaces in nonzero space form have constant mean curvature},
author = {Zhida Guan and Haizhong Li and Luc Vrancken},
journal= {arXiv preprint arXiv:2007.13589},
year = {2020}
}