{"paper":{"title":"Non-isoparametric solutions of the eikonal equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Vladimir G. Tkachev","submitted_at":"2010-09-09T18:23:13Z","abstract_excerpt":"In this paper, we prove that a quartic polynomial solution of the eikonal equation $|\\nabla_x f|^2=16x^{6}$ in $\\R{n}$ is either an isoparametric polynomial or congruent to a polynomial $f=(\\sum_{i=1}^n x_i^2)^2-8(\\sum_{i=1}^k x_i^2)(\\sum_{i=k+1}^{n} x_i^2)$, $k=0,1,\\...,[\\frac{n}{2}]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1842","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"}