{"paper":{"title":"Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Brendan Guilfoyle, Henri Anciaux, Pascal Romon","submitted_at":"2008-07-09T07:15:01Z","abstract_excerpt":"Given an oriented Riemannian surface $(\\Sigma, g)$, its tangent bundle $T\\Sigma$ enjoys a natural pseudo-K\\\"{a}hler structure, that is the combination of a complex structure $\\J$, a pseudo-metric $\\G$ with neutral signature and a symplectic structure $\\Om$. We give a local classification of those surfaces of $T\\Sigma$ which are both Lagrangian with respect to $\\Om$ and minimal with respect to $\\G$. We first show that if $g$ is non-flat, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.1387","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"}