New results toward the classification of biharmonic submanifolds in 𝕊n

Abstract

Abstract We prove some new rigidity results for proper biharmonic immer- sions in Sn of the following types: Dupin hypersurfaces; hypersurfaces, both compact and non-compact, with bounded norm of the second fun- damental form; hypersurfaces satisfying intrinsic properties; PMC sub- manifolds; parallel submanifolds.