# Willmore spacelike submanifolds in a Lorentzian space form $N^{n p} pc$

Willmore spacelike submanifolds in a Lorentzian space form $N^{n p} pc$ - Download this document for free, or read online. Document in PDF available to download.

Mathematical Communications, Vol.19 No.2 December 2014. -

Let $N^{n+p} pc$ be an $n+p$-dimensional connected Lorentzian space form of constant sectional curvature $c$ and $\varphi: M ightarrow N^{n+p} pc$ an $n$-dimensional spacelike submanifold in $N^{n+p} pc$. The immersion $\varphi: M ightarrow N^{n+p} pc$ is called a Willmore spacelike submanifold in $N^{n+p} pc$ if it is a critical submanifold to the Willmore functional \W\varphi=\int M ho^ndv=\int MS-nH^2^{\frac{n}{2}}dv,\

where $S$, $H$ and $ ho^2$ denote the norm square of the second fundamental form, the mean curvature and the non-negative function

$ ho^2=S-nH^2$ of $M$. In this article, by calculating the first variation of $W\varphi$, we obtain the Euler-Lagrange equation of $W\varphi$ and prove some rigidity theorems for $n$-dimensional Willmore spacelike submanifolds in $N^{n+p} pc$.

Willmore spacelike submanifold; Lorentzian space form; Euler-Lagrange equation; totally umbilical

Author: ** Shichang Shu - Junfeng Chen - **

Source: http://hrcak.srce.hr/