{"paper":{"title":"Two remarks on $PQ^{\\epsilon}$-projectivity of Riemannian metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Stefan Rosemann, Vladimir S. Matveev","submitted_at":"2011-08-15T10:23:46Z","abstract_excerpt":"We show that $PQ^{\\epsilon}$-projectivity of two Riemannian metrics introduced in \\cite{Top2003} implies affine equivalence of the metrics unless $\\epsilon\\in\\{0,-1,-3,-5,-7,...\\}$. Moreover, we show that for $\\epsilon=0$, $PQ^{\\epsilon}$-projectivity implies projective equivalence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2965","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"}