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

A. Balmus; S. Montaldo; C. Oniciuc

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

Differential Geometry 2012-03-20 v2

Authors: A. Balmus , S. Montaldo , C. Oniciuc

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.

Keywords

biharmonic submanifolds rigidity results Dupin hypersurfaces second fundamental form PMC submanifolds parallel submanifolds sphere

Cite

@article{arxiv.1111.6063,
  title  = {New results toward the classification of Biharmonic submanifolds in $\mathbb{S}^{n}$},
  author = {A. Balmus and S. Montaldo and C. Oniciuc},
  journal= {arXiv preprint arXiv:1111.6063},
  year   = {2012}
}

Comments

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

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

Abstract

Keywords

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