{"paper":{"title":"Ricci curvature of double manifolds via isoparametric foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chao Qian, ChiaKuei Peng","submitted_at":"2016-01-13T04:24:24Z","abstract_excerpt":"Given a closed manifold $M$ and a vector bundle $\\xi$ of rank $n$ over $M$, by gluing two copies of the disc bundle of $\\xi$, we can obtain a closed manifold $D(\\xi, M)$, the so-called double manifold.\n  In this paper, we firstly prove that each sphere bundle $S_r(\\xi)$ of radius $r>0$ is an isoparametric hypersurface in the total space of $\\xi$ equipped with a connection metric, and for $r>0$ small enough, the induced metric of $S_r(\\xi)$ has positive Ricci curvature under the additional assumptions that $M$ has a metric with positive Ricci curvature and $n\\geq3$.\n  As an application, if $M$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03125","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"}