{"paper":{"title":"On Hamiltonian minimal submanifolds in the space of oriented geodesics in real space forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guillermo Antonio Lobos Villagra, Nikos Georgiou","submitted_at":"2014-11-29T20:06:21Z","abstract_excerpt":"We prove that a deformation of a hypersurface in a $(n+1)$-dimensional real space form ${\\mathbb S}^{n+1}_{p,1}$ induce a Hamiltonian variation of the normal congruence in the space ${\\mathbb L}({\\mathbb S}^{n+1}_{p,1})$ of oriented geodesics. As an application, we show that every Hamiltonian minimal sumbanifold in ${\\mathbb L}({\\mathbb S}^{n+1})$ (resp. ${\\mathbb L}({\\mathbb H}^{n+1})$) with respect to the (para-) Kaehler Einstein structure is locally the normal congruence of a hypersurface $\\Sigma$ in ${\\mathbb S}^{n+1}$ (resp. ${\\mathbb H}^{n+1}$) that is a critical point of the functional "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0147","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"}