{"paper":{"title":"Real hypersurfaces in the complex quadric with Reeb parallel structure Jacobi operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hyunjin Lee, Young Jin Suh","submitted_at":"2019-07-09T00:46:28Z","abstract_excerpt":"In this paper, we first introduce the full express of the Riemannian curvature tensor of a real hypersurface $M$ in complex quadric $Q^{m}$ from the equation of Gauss. Next we derive a formula for the structure Jacobi operator $R_{\\xi}$ and its derivative under the Levi-Civita connection of $M$. We give a complete classification of Hopf real hypersurfaces with Reeb parallel structure Jacobi operator, $\\nabla_{\\xi}R_{\\xi} =0$, in the complex quadric $Q^{m}$, $m \\geq 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04661","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"}