{"paper":{"title":"A lower bound of the energy functional of a class of vector fields and a characterization of the sphere","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Giovanni da Silva Nunes, Jaime Ripoll","submitted_at":"2025-04-26T17:27:37Z","abstract_excerpt":"Let $M$ be a compact, orientable, $n$-dimensional Riemannian manifold, $n\\geq2$, and let $F$ be the energy functional acting on the space $\\Xi (M)$ of $C^{\\infty }$ vector fields of $M$,\n  \\[ F(X):=\\frac{\\int_{M}\\left\\Vert \\nabla X\\right\\Vert ^{2}dM}{\\int_{M}\\left\\Vert X\\right\\Vert ^{2}dM}, X\\in \\Xi (M)\\backslash\\{0\\}. % \\]\n  Let $G\\in\\operatorname*{Iso}\\left(M\\right)$ be a compact Lie subgroup of the isometry group of $M$ acting with cohomogeneity $1$ on $M$. Assume that any isotropy subgroup of $G$ is non trivial and acts with no fixed points on the tangent spaces of $M$, except at the null "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.18975","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.18975/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}