{"paper":{"title":"Geometric interpretation of generalized distance-squared mappings of $\\mathbb{R}^2$ into $\\mathbb{R}^\\ell$ $(\\ell \\geq 3)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shunsuke Ichiki","submitted_at":"2017-01-27T04:17:13Z","abstract_excerpt":"Generalized distance-squared mappings are quadratic mappings of $\\mathbb{R}^m$ into $\\mathbb{R}^\\ell$ of special type. In the case that matrices $A$ constructed by coefficients of generalized distance-squared mappings of $\\mathbb{R}^2$ into $\\mathbb{R}^\\ell$ ($\\ell \\geq3$) are full rank, the generalized distance-squared mappings having a generic central point have the following properties. In the case of $\\ell=3$, they have only one singular point. On the other hand, in the case of $\\ell>3$, they have no singular points. Hence, in this paper, the reason why in the case of $\\ell=3$ (resp., in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07938","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"}