Biharmonic conjectures on hypersurfaces in a space form

Abstract

We apply the Murnaghan-Nakayama rule in the representation theory of symmetric groups to develop new techniques for studying biharmonic hypersurfaces in a space form. As applications of the new techniques, we settle the well-known Chen’s conjecture on biharmonic hypersurfaces in R 6 \Bbb R^6 and BMO conjecture on biharmonic hypersurfaces in S 6 \mathbb S^6 .