{"paper":{"title":"Almost complex surfaces in the nearly K\\\"ahler $S^3\\times S^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bart Dioos, Franki Dillen, John Bolton, Luc Vrancken","submitted_at":"2012-08-03T13:31:04Z","abstract_excerpt":"In this paper almost complex surfaces of the nearly K\\\"ahler $S^3\\times S^3$ are studied in a systematic way. We show that on such a surface it is possible to define a global holomorphic differential, which is induced by an almost product structure on the nearly K\\\"ahler $S^3\\times S^3$. We also find a correspondence between almost complex surfaces in the nearly K\\\"ahler $S^3\\times S^3$ and solutions of the general $H$-system equation introduced by Wente, thus obtaining a geometric interpretation of solutions of the general $H$-system equation. From this we deduce a correspondence between cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0737","kind":"arxiv","version":4},"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"}