Conformal geometry of marginally trapped surfaces in \(\mathbb {S}^4_1\) (Q515726)

A space-like surface immersed in a 4D Lorentzian manifold is called \textit{marginally trapped} if its mean curvature vector is everywhere null or light-like. This notion was introduced by Penrose and plays a key role in the singularity theory of Einstein equations. The purpose of this work is to study geometric properties of oriented marginally trapped surfaces conformally immersed in \(\mathbb {S}^4_1\) by using complex analysis, including also the construction of a suitable \textit{null Gauss map}. The conformal invariants of these maps are computed in order to obtain results regarding the congruence of marginally trapped surfaces in \(\mathbb {S}^4_1\).