%0 Journal Article
%T Biharmonic submanifolds with parallel mean curvature in $\mathbb{S}^n\times\mathbb{R}$
%A Dorel Fetcu
%A Cezar Oniciuc
%A Harold Rosenberg
%J Mathematics
%D 2011
%I arXiv
%X 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 $\mathbb{S}^n(c)\times\mathbb{R}$.
%U http://arxiv.org/abs/1109.6138v1