Publications de l’Institut Mathématique, Nouvelle Série Vol. 102[116], pp. 175–193 (2017) 

Willmore spacelike submanifolds in an indefinite space form ${N}_{q}^{n+p}\left(c\right)$Shichang Shu, Junfeng ChenSchool of Mathematics and Information Science, Xianyang Normal University, Xianyang, P.R. ChinaAbstract: Let ${N}_{q}^{n+p}\left(c\right)$ be an $(n+p)$dimensional connected indefinite space form of index $q$ $(1\le q\le p)$ and of constant curvature $c$. Denote by $\phi :M\to {N}_{q}^{n+p}\left(c\right)$ the $n$dimensional spacelike submanifold in ${N}_{q}^{n+p}\left(c\right)$, $\phi :M\to {N}_{q}^{n+p}\left(c\right)$ is called a Willmore spacelike submanifold in ${N}_{q}^{n+p}\left(c\right)$ if it is a critical submanifold to the Willmore functional $W\left(\phi \right)={\int}_{M}{\rho}^{n}dv={\int}_{M}{(Sn{H}^{2})}^{\frac{n}{2}}dv$, where $S$ and $H$ denote the norm square of the second fundamental form and the mean curvature of $M$ and ${\rho}^{2}=Sn{H}^{2}$. If $q=p$, in Keywords: indefinite space form, Willmore spacelike submanifold, totally umbilical, EulerLagrange equation Classification (MSC2000): 53C42; 53C40 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 3 Nov 2017. This page was last modified: 29 Jan 2018.
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