{"paper":{"title":"Metrics of constant scalar curvature on sphere bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jimmy Petean, Nobuhiko Otoba","submitted_at":"2015-06-04T06:44:33Z","abstract_excerpt":"Let $G/H$ be a Riemannian homogeneous space. For an orthogonal representation $\\phi$ of $H$ on the Euclidean space $\\mathbb{R}^{k+1}$, there corresponds the vector bundle $E=G\\times_{\\phi}\\mathbb{R}^{k+1} \\to G/H$ with fiberwise inner product. Provided that $\\phi$ is the direct sum of at most two representations which are either trivial or irreducible, we construct metrics of constant scalar curvature on the unit sphere bundle $UE$ of $E$. When $G/H$ is the round sphere, we study the number of constant scalar curvature metrics in the conformal classes of these metrics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01474","kind":"arxiv","version":2},"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"}