{"paper":{"title":"On the structure of complete k\\\"ahlerian manifolds furnished with closed conformal vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antonio Caminha","submitted_at":"2014-09-19T12:42:53Z","abstract_excerpt":"We show that if a connected compact k\\\"ahlerian surface $M$ with nonpositive gaussian curvature is furnished with a closed conformal vector field $\\xi$ whose singular points are isolated, then $M$ is isometric to a flat torus and $\\xi$ is parallel. We also consider the case of a connected complete k\\\"ahlerian manifod $M$ of complex dimension $n>1$ and furnished with a nontrivial closed conformal vector field $\\xi$. In this case, it is well known that the singularities of $\\xi$ are automatically isolated and the nontrivial leaves of the distribution generated by $\\xi$ and $J\\xi$ are totally geo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5629","kind":"arxiv","version":3},"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"}