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

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

2011-11-25

arxiv.org/abs/1111.6063v2

Mathematics

Differential Geometry

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

Scientific paper

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.

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