Shun Maeta, Ye-Lin Ou
Published 2017-08-28Version 1
We give some classifications of biharmonic hypersurfaces with constant scalar curvature. These include biharmonic Einstein hypersurfaces in space forms, compact biharmonic hypersurfaces with constant scalar curvature in a sphere, and some complete biharmonic hypersurfaces of constant scalar curvature in space forms and in a non-positively curved Einstein space. Our results provide additional cases (Theorem 2.3 and Proposition 2.8) that supports the conjecture that a biharmonic submanifold in a sphere has constant mean curvature, and two more cases that support Chen's conjecture on biharmonic hypersurfaces (Corollaries 2.2,2.7).
Geometric realizations of curvature models by manifolds with constant scalar curvature
On biharmonic hypersurfaces with constant scalar curvatures in $\mathbb E^5(c)$
Construction of Kaehler surfaces with constant scalar curvature
![QR code for arXiv:1708.08540 [math.DG]](http://oss.arxitics.com/images/favicon.svg)