{"paper":{"title":"Real hypersurfaces in $Q^m$ with commuting structure Jacobi operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"M.J. Vanaei, N. Heidari, S.M.B. Kashani","submitted_at":"2018-07-29T08:08:20Z","abstract_excerpt":"In this paper we study real hypersurfaces in the complex quadric space $Q^m$ whose structure Jacobi operator commutes with their structure tensor field. We show that the Reeb curvature $\\alpha$ of such hypersurfaces is constant and if $\\alpha$ is non-zero then the hypersurface is a tube around a totally geodesic submanifold $\\mathbb{C} P^k \\subset Q^m$, where $m=2k$. We also consider Reeb flat hypersurfaces, namely, when the Reeb curvature is zero. We show that the tube around $\\mathbb{C} P^k \\subset Q^m$ ($m=2k$), with radius $\\frac{\\pi}{4}$ is the only Reeb flat Hopf hypersurface with commut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11021","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"}