arXiv:1111.6063 Abstract | arXiv Analytics

arXiv:1111.6063 [math.DG]Abstract References Reviews Resources

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

Published 2011-11-25, updated 2012-03-19Version 2

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.

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

Categories: math.DG

Keywords: biharmonic submanifolds, classification, proper biharmonic immersions, hypersurfaces satisfying intrinsic properties, second fundamental form

Related articles: Most relevant | Search more

arXiv:1801.07879 [math.DG] (Published 2018-01-24)

Bochner-Simons formulas and the rigidity of biharmonic submanifolds

Dorel Fetcu, Eric Loubeau, Cezar Oniciuc

arXiv:1010.5488 [math.DG] (Published 2010-10-26, updated 2011-01-24)

On the classification of warped product Einstein metrics

Chenxu He, Peter Petersen, William Wylie

arXiv:1109.6138 [math.DG] (Published 2011-09-28)

Biharmonic submanifolds with parallel mean curvature in $\mathbb{S}^n\times\mathbb{R}$