{"paper":{"title":"Behavior of Gaussian curvature and mean curvature near non-degenerate singular points on wave fronts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kentaro Saji, Kotaro Yamada, Luciana F. Martins, Masaaki Umehara","submitted_at":"2013-08-09T14:31:30Z","abstract_excerpt":"We define cuspidal curvature $\\kappa_c$ (resp. normalized cuspidal curvature $\\mu_c$) along cuspidal edges (resp. at swallowtail singularity) in Riemannian $3$-manifolds, and show that it gives a coefficient of the divergent term of the mean curvature function. Moreover, we show that the product $\\kappa_\\Pi$ called the product curvature (resp. $\\mu_\\Pi$ called normalized product curvature) of $\\kappa_c$ (resp. $\\mu_c$) and the limiting normal curvature $\\kappa_\\nu$ is an intrinsic invariant of the surface, and is closely related to the boundedness of the Gaussian curvature. We also consider th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2136","kind":"arxiv","version":6},"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"}