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

A. Balmus; S. Montaldo; C. Oniciuc

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arXiv · 1111.6063

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

A. Balmus·S. Montaldo·C. Oniciuc

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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.

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BibTeX RIS

A. Balmus, S. Montaldo, C. Oniciuc. 2011-11-25. New results toward the classification of Biharmonic submanifolds in $\mathbb{S}^{n}$. https://arxiv.org/abs/1111.6063

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