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

Dorel Fetcu; Cezar Oniciuc; Harold Rosenberg

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

Differential Geometry 2011-09-29 v1

Authors: Dorel Fetcu , Cezar Oniciuc , Harold Rosenberg

Abstract

We find a Simons type formula for submanifolds with parallel mean curvature vector (pmc submanifolds) in product spaces $M^n(c)\times\mathbb{R}$ , where $M^n(c)$ is a space form with constant sectional curvature $c$ , and then we use it to prove a gap theorem for the mean curvature of certain complete proper-biharmonic pmc submanifolds, and classify proper-biharmonic pmc surfaces in $\mathbb{S}^n(c)\times\mathbb{R}$ .

Keywords

biharmonic submanifolds parallel mean curvature Simons type formula product spaces gap theorem space form

Cite

@article{arxiv.1109.6138,
  title  = {Biharmonic submanifolds with parallel mean curvature in $\mathbb{S}^n\times\mathbb{R}$},
  author = {Dorel Fetcu and Cezar Oniciuc and Harold Rosenberg},
  journal= {arXiv preprint arXiv:1109.6138},
  year   = {2011}
}

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15 pages

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

Abstract

Keywords

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