{"paper":{"title":"Compact complex surfaces with geometric structures related to split quaternions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.DG","authors_text":"Gueo Grantcharov, Johann Davidov, Miroslav Yotov, Oleg Mushkarov","submitted_at":"2012-05-11T17:07:00Z","abstract_excerpt":"We study the problem of existence of geometric structures on compact complex surfaces that are related to split quaternions. These structures, called para-hypercomplex, para-hyperhermitian and para-hyperk\\\"ahler are analogs of the hypercomplex, hyperhermitian and hyperk\\\"ahler structures in the definite case. We show that a compact oriented 4-manifold carries a para-hyperk\\\"ahler structure iff it has a metric of split signature together with two parallel, orthogonal and null vector fields. Every compact complex surface admiting a para-hyperhermitian structure has vanishing first Chern class an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2580","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"}