{"paper":{"title":"On minimal Lagrangian surfaces in the product of Riemannian two manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Nikos Georgiou","submitted_at":"2013-05-07T15:34:22Z","abstract_excerpt":"Let $(\\Sigma_1,g_1)$ and $(\\Sigma_2,g_2)$ be connected, complete and orientable Riemannian two manifolds. Consider the two canonical K\\\"ahler structures $(G^{\\epsilon},J,\\Omega^{\\epsilon})$ on the product 4-manifold $\\Sigma_1\\times\\Sigma_2$ given by $ G^{\\epsilon}=g_1\\oplus \\epsilon g_2$, $\\epsilon=\\pm 1$ and $J$ is the canonical product complex structure. Thus for $\\epsilon=1$ the K\\\"ahler metric $G^+$ is Riemannian while for $\\epsilon=-1$, $G^-$ is of neutral signature. We show that the metric $G^{\\epsilon}$ is locally conformally flat iff the Gauss curvatures $\\kappa(g_1)$ and $\\kappa(g_2)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1561","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"}