{"paper":{"title":"Hypersurfaces with light-like points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kotaro Yamada, Masaaki Umehara","submitted_at":"2018-06-24T23:17:43Z","abstract_excerpt":"Consider a constant mean curvature immersion $F:U(\\subset \\boldsymbol{R}^n)\\to M$ into an arbitrary Lorentzian $(n+1)$-manifold $M$. A point $o\\in U$ is called a light-like point if the first fundamental form $ds^2$ of $F$ degenerates at $o$. We denote by $B_F$ the determinant function of the symmetric matrix associated to $ds^2$ with respect to a local coordinate system at $o$. A light-like point $o$ is said to be degenerate if the exterior derivative of $B_F$ vanishes at $o$. We show that if $o$ is a degenerate light-like point, then the image of $F$ contains a light-like geodesic segment of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09233","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}