{"paper":{"title":"On the critical points of the energy functional on vector fields of a Riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Giovanni Nunes, Jaime Ripoll","submitted_at":"2016-11-21T21:25:11Z","abstract_excerpt":"Given a compact Lie subgroup $G$ of the isometry group of a compact Riemannian manifold $M$ with a Riemannian connection $\\nabla,$ it is introduced a $G-$symmetrization process of a vector field of $M$ and it is proved that the critical points of the energy functional \\[ F(X):=\\frac{\\int_{M}\\left\\Vert \\nabla X\\right\\Vert ^{2}dM}{\\int_{M}\\left\\Vert X\\right\\Vert ^{2}dM}% \\] on the space of $\\ G-$invariant vector fields are critical points of $F$ on the space of all vector fields of $M,$ and that this inclusion may be strict in general. One proves that the infimum of $F$ on $\\mathbb{S}^{3}$ is no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07066","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"}