{"paper":{"title":"On the geometry of almost Golden Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Abhitosh Upadhyay, Fernando Etayo, Rafael Santamar\\'ia","submitted_at":"2017-04-04T09:14:30Z","abstract_excerpt":"An almost Golden Riemannian structure $(\\varphi ,g)$ on a manifold is given by a tensor field $\\varphi $ of type (1,1) satisfying the Golden section relation $\\varphi ^{2}=\\varphi +1$, and a pure Riemannian metric $g$, i.e., a metric satisfying $g(\\varphi X,Y)=g(X,\\varphi Y)$. We study connections adapted to such a structure, finding two of them, the first canonical and the well adapted, which measure the integrability of $\\varphi $ and the integrability of the $G$-structure corresponding to $(\\varphi ,g)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00926","kind":"arxiv","version":1},"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"}