{"paper":{"title":"Anti-orthotomics of frontals and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Stanis{\\l}aw Janeczko, Takashi Nishimura","submitted_at":"2019-06-26T13:27:21Z","abstract_excerpt":"Let $f: N^n\\to \\mathbb{R}^{n+1}$ be a frontal with its Gauss mapping $\\nu: N\\to S^n$ and let $P\\in \\mathbb{R}^{n+1}$ be a point such that $(f(x)-P)\\cdot \\nu(x) \\ne 0$ for any $x\\in N$. In this paper, for the mapping $\\widetilde{f}: N\\to \\mathbb{R}^{n+1}$ defined by $$ \\widetilde{f}(x)=f(x)-\\frac{||f(x)-P||^2}{2(f(x)-P) \\cdot \\nu(x)}\\nu(x), $$ the following four are shown. (1) $\\widetilde{f}$ is a frontal with its Gauss mapping $\\widetilde{\\nu}(x)=\\frac{f(x)-P}{||f(x)-P||}$ at $\\widetilde{f}(x)$. (2) $\\widetilde{f}$ is the unique anti-orthotomic of $f$ relative to $P$. (3) The property $(\\widet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00721","kind":"arxiv","version":2},"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"}