{"paper":{"title":"Gauss map and the topology of constant mean curvature hypersurfaces of $\\mathbb{S}^{7}$ and $\\mathbb{CP}^{3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Eduardo Longa, Fidelis Bittencourt, Jaime Ripoll, Pedro Fusieger","submitted_at":"2017-03-07T19:12:34Z","abstract_excerpt":"We define a Gauss map $\\gamma:M\\rightarrow\\mathbb{S}^{6}$ of an oriented hypersurface $M$ of the unit sphere $\\mathbb{S}^{7}$ and prove that $\\gamma$ is harmonic if and only if $M$ has CMC. Results on the geometry and topology of CMC hypersurfaces of $\\mathbb{S}^{7}$, under hypothesis on the image of $\\gamma$, are then obtained. By a Hopf symmetrization process we define a Gauss map for hypersurfaces of $\\mathbb{CP}^{3}$ and obtain similar results for CMC hypersurfaces of this space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02560","kind":"arxiv","version":5},"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"}