{"paper":{"title":"Extremal conformal structures on projective surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.GT"],"primary_cat":"math.DG","authors_text":"Thomas Mettler","submitted_at":"2015-10-05T06:43:26Z","abstract_excerpt":"We introduce a new functional $\\mathcal{E}_{\\mathfrak{p}}$ on the space of conformal structures on an oriented projective manifold $(M,\\mathfrak{p})$. The nonnegative quantity $\\mathcal{E}_{\\mathfrak{p}}([g])$ measures how much $\\mathfrak{p}$ deviates from being defined by a $[g]$-conformal connection. In the case of a projective surface $(\\Sigma,\\mathfrak{p})$, we canonically construct an indefinite K\\\"ahler--Einstein structure $(h_{\\mathfrak{p}},\\Omega_{\\mathfrak{p}})$ on the total space $Y$ of a fibre bundle over $\\Sigma$ and show that a conformal structure $[g]$ is a critical point for $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01043","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1510.01043/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}