On biharmonic hypersurfaces with constant scalar curvatures in $\mathbb E^5(c)$
Differential Geometry
2014-12-24 v1
Abstract
We prove that proper biharmonic hypersurfaces with constant scalar curvature in Euclidean sphere must have constant mean curvature. Moreover, we also show that there exist no proper biharmonic hypersurfaces with constant scalar curvature in Euclidean space or hyperbolic space , which give affirmative partial answers to Chen's conjecture and Generalized Chen's conjecture.
Keywords
Cite
@article{arxiv.1412.7394,
title = {On biharmonic hypersurfaces with constant scalar curvatures in $\mathbb E^5(c)$},
author = {Yu Fu},
journal= {arXiv preprint arXiv:1412.7394},
year = {2014}
}
Comments
11 pages, to appear in Proc. Amer. Math. Soc. arXiv admin note: text overlap with arXiv:1412.5726