#### Vol. 306, No. 1, 2020

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Some classifications of biharmonic hypersurfaces with constant scalar curvature

### Shun Maeta and Ye-Lin Ou

Vol. 306 (2020), No. 1, 281–290
##### Abstract

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 nonpositively curved Einstein space. Our results provide additional cases (Theorem 2.3 and Proposition 2.8) that support the conjecture that a biharmonic submanifold in ${S}^{m+1}$ has constant mean curvature, and two more cases that support Chen’s conjecture on biharmonic hypersurfaces (Corollaries 2.2 and 2.7).

##### Keywords
biharmonic hypersurfaces, Einstein manifolds, constant scalar curvature, constant mean curvature
Primary: 58E20
Secondary: 53C12