{"paper":{"title":"Killing vector fields of constant length on compact hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antonio J. Di Scala","submitted_at":"2013-07-19T08:36:29Z","abstract_excerpt":"We show that if a compact hypersurface $M \\subset \\mathbb{R}^{n+1}$, $n \\geq3$, admits a non zero Killing vector field $X$ of constant length then $n$ is even and $M$ is diffeomorphic to the unit hypersphere of $\\mathbb{R}^{n+1}$. Actually, we show that $M$ is a complex ellipsoid in $\\mathbb{C}^{N} = \\mathbb{R}^{n+1}$. As an application we give a simpler proof of a recent theorem due to S. Deshmukh \\cite{De12}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5160","kind":"arxiv","version":3},"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"}