부산대학교 도서관

Let $M$ be a surface in a Lorentzian space form $\Bbb{R}_1^4(c)$ of constant sectional curvature $c$ and let $h$ be the second fundamental form. According as $c=0, 1, -1$ we have $\Bbb{E}_1^4$, $\Bbb{S}_1^4$ and $\Bbb{H}_1^4$, Minkowski, de Sitter and anti-de Sitter spacetime, respectively. The relative null space at a point $p \in M$ is defined by $\scr{N}_p(M)=\{X \in T_pM \,\colon \, h(X,Y)=0$ for all $Y \in T_pM\}$. Then $\nu_p=\dim(\scr{N}_p(M))$ is called the relative nullity at $p$ and $M$ is said to have positive relative nullity if $\nu_p>0$ for each $p\in M$. In the realm of general relativity, a spacelike surface in a 4-dimensional Lorentzian manifold is called marginally trapped when its mean curvature vector is lightlike at each point. The main result of this paper states that, up to isometries of $\Bbb{E}_1^4$, there exist two families of marginally trapped spacelike surfaces with positive relative nullity in $\Bbb{E}_1^4$. The paper concludes by exhibiting both families in $\Bbb{S}_1^4$ and $\Bbb{H}_1^4$.