On biharmonic hypersurfaces with constant scalar curvatures in ${\mathbb{E}}^5(c)$

Abstract

We prove that proper biharmonic hypersurfaces with constant scalar curvature in Euclidean sphere ${\mathbb{S}}^5$ must have constant mean curvature. Moreover, we also show that there exist no proper biharmonic hypersurfaces with constant scalar curvature in Euclidean space ${\mathbb{E}}^5$ or hyperbolic space ${\mathbb{H}}^5$, which give affirmative partial answers to Chen's conjecture and Generalized Chen's conjecture.

11 pages, to appear in Proc. Amer. Math. Soc. arXiv admin note: text overlap with arXiv:1412.5726