New results toward the classification of Biharmonic submanifolds in ${\mathbb{S}}^n$

Abstract

We prove some new rigidity results for proper biharmonic immersions in ${\mathbb{S}}^n$ of the following types: Dupin hypersurfaces; hypersurfaces, both compact and non-compact, with bounded norm of the second fundamental form; hypersurfaces satisfying intrinsic properties; PMC submanifolds; parallel submanifolds.

arXiv comment18 pages. Final Version to appear in Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica