{"paper":{"title":"A sufficient condition for a hypersurface to be isoparametric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dongyi Wei, Wenjiao Yan, Zizhou Tang","submitted_at":"2018-03-27T10:43:05Z","abstract_excerpt":"Let $M^n$ be a closed Riemannian manifold on which the integral of the scalar curvature is nonnegative. Suppose $\\mathfrak{a}$ is a symmetric $(0,2)$ tensor field whose dual $(1,1)$ tensor $\\mathcal{A}$ has $n$ distinct eigenvalues, and $\\mathrm{tr}(\\mathcal{A}^k)$ are constants for $k=1,\\cdots, n-1$. We show that all the eigenvalues of $\\mathcal{A}$ are constants, generalizing a theorem of de Almeida and Brito \\cite{dB90} to higher dimensions.\n  As a consequence, a closed hypersurface $M^n$ in $S^{n+1}$ is isoparametric if one takes $\\mathfrak{a}$ above to be the second fundamental form, givi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10006","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"}