CORRIGENDUM: CODIMENSION-TWO SPACELIKE SUBMANIFOLDS WITH UMBILICAL LIGHTLIKE NORMAL SECTIONS AND THEIR RELATIONSHIP TO LIGHTLIKE

Abstract

This corrigendum corrects an error in the proof of Theorem 6.20 of the original article. Property (P), used to propagate umbilicity from the initial spacelike submanifold to the lightlike hypersurface generated by the normal exponential map, is false, and an explicit counterexample shows that the corresponding implication fails in a general spacetime. The normal exponential construction, the geodesic lightlike extension, the associated integrable screen distribution, and the leafwise characterization of total umbilicity remain valid. We state the corrected form of Theorem 6.20 and show that the original umbilicity conclusion is recovered when the ambient spacetime is locally conformally flat. The necessary amendments to the subsequent results are also recorded.