{"paper":{"title":"A relation between the curvature ellipse and the curvature parabola","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Pedro Benedini Riul, Ra\\'ul Oset Sinha","submitted_at":"2017-08-15T19:05:37Z","abstract_excerpt":"At each point in an immersed surface in $\\mathbb R^4$ there is a curvature ellipse in the normal plane which codifies all the local second order geometry of the surface. More recently, at the singular point of a corank 1 singular surface in $\\mathbb R^3$, a curvature parabola in the normal plane which codifies all the local second order geometry has been defined. When projecting a regular surface in $\\mathbb R^4$ to $\\mathbb R^3$ in a tangent direction corank 1 singularities appear generically. The projection has a cross-cap singularity unless the direction of projection is asymptotic, where m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04651","kind":"arxiv","version":1},"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"}