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

Dorel Fetcu; Cezar Oniciuc; Harold Rosenberg

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arXiv · 1109.6138

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

Dorel Fetcu·Cezar Oniciuc·Harold Rosenberg

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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 $\mathbb{S}^n(c)\times\mathbb{R}$.

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BibTeX RIS

Dorel Fetcu, Cezar Oniciuc, Harold Rosenberg. 2011-09-28. Biharmonic submanifolds with parallel mean curvature in $\mathbb{S}^n\times\mathbb{R}$. https://arxiv.org/abs/1109.6138

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