{"paper":{"title":"Minimal isoparametric submanifolds of $\\mathbb{S}^{7}$ and octonionic eigenmaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Daniel Bustos, Edson Figueiredo, Fidelis Bittencourt, Jaime Ripoll, Pedro Fusieger","submitted_at":"2018-08-21T08:54:33Z","abstract_excerpt":"We use the octonionic multiplication $\\cdot$ of $\\mathbb{S}^{7}$ to associate, to each unit normal section $\\eta$ of a submanifold $M$ of $\\mathbb{S}^{7},$ an octonionic Gauss map $\\gamma_{\\eta}:M\\rightarrow\\mathbb{S}^{6},$ $\\gamma_{\\eta}(x)=x^{-1}\\cdot\\eta(x),$ $x\\in M,$ where $\\mathbb{S}^{6}$ is the unit sphere of $T_{1}\\mathbb{S}^{7},$ $1$ is the neutral element of $\\cdot$ in $\\mathbb{S}^{7}.$ Denoting by $\\mathcal{N}(M)$ the vector bundle of normal sections of $M$ we set, for $\\eta$ $\\in\\mathcal{N}(M),$ $S_{\\eta}(X)=-\\left(\\nabla_{X}\\eta\\right) ^{\\top},$ $X\\in TM.$ Considering the Hilbert-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06802","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"}