SOME CLASSIFICATIONS OF BIHARMONIC HYPERSURFACES WITH CONSTANT SCALAR CURVATURE

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 Sm+1 has constant mean curvature, and two more cases that support Chen’s conjecture on biharmonic hypersurfaces (Corollaries 2.2 and 2.7).