{"paper":{"title":"Spherical orthotomic curve-germs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Takashi Nishimura, Xihe Liu","submitted_at":"2019-01-14T06:46:42Z","abstract_excerpt":"In this paper, it is shown that for an $n$-dimensional spherical unit speed curve $\\gamma: I\\to S^n$, a given point $P \\in S^n$ and a point $s_0$ of the open interval $I$, the spherical orthotomic curve-germ $ort_{\\gamma, P}: (I, s_0)\\to S^n$ of $\\gamma$ relative to $P$ is $\\mathcal{L}$-equivalent to the spherical pedal curve-germ $ped_{\\gamma, P}: (I, s_0)\\to S^n$ of $\\gamma$ relative to $P$ (resp., the spherical dual curve-germ ${\\bf u}_n: (I, s_0)\\to S^n$ of $\\gamma$) if and only if $P\\ne \\pm{\\bf u}_n(s_0)$ (resp., if $P= \\pm{\\bf u}_n(s_0)$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04150","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"}