# Marginally Trapped surfaces with constant Gaussian curvature

By marginally trapped surface I mean a spacelike surface in a 4-dimensional Lorentzian manifold such that the mean curvature vector is lightlike.

In my research I have stumbled across marginally trapped surfaces with Gaussian curvature equal to 1 in De Sitter's space. I have searched in vain for references about such surfaces. Does anyone know anything about them and if they could be interesting for General Relativity? I also have stumbled across spacelike surfaces with flat normal bundle in De Sitter space with constant Gaussian equal to 1, same question... Thank you in advance for any information.

If by De Sitter you mean the manifold isometric to the exterior hyperboloid embedded in 4+1 dimensional Minkowski space: the section $t = 0$ is totally geodesic and isometric to $\mathbb{S}^3$. The equator of $\mathbb{S}^3$ is a minimal surface, and hence is a marginally trapped surface in de Sitter space. Furthermore, as the equator in $\mathbb{S}^3$ it is isometric to $\mathbb{S}^2$ and hence has constant Gaussian curvature.