An Alexandrov theorem in Minkowski spacetime (Q2194543)

A codimension-two submanifold \(\Sigma\) of a Lorentzian manifold is said to have constant normalized null curvature (CNNC) if there exists a future null normal vector field \(\mathcal L\) such that \(\Sigma\) is torsion-free with respect to \(L\) and \(\langle\mathcal H, \mathcal L\rangle\) is a constant, where \(\mathcal H\) denotes the mean curvature vector field on \(\Sigma^n\). In the paper, using a spinorial approach developed by the first two authors and \textit{X. Zhang}, the authors generalize a theorem à la Alexandrov of [J. Differ. Geom. 105, No. 2, 249--290 (2017; Zbl 1380.53089)] to closed codimension-two space-like submanifolds in the Minkowski spacetime for an adapted CMC condition. In particular, they prove that if \(\Sigma\) is an untrapped codimension-two submanifold in the Minkowski spacetime and suppose that \(\Sigma\) has CNNC with respect to a future null normal vector field \(\mathcal L\), then \(\Sigma\) lies in a shearfree null hypersurface.