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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.01474","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-04T06:44:33Z","cross_cats_sorted":[],"title_canon_sha256":"29489f366b90734421c195739142bc54eff3c85227f8a77c95980bfb94a9759f","abstract_canon_sha256":"95e161e0a965759cbcb74dd015306bc050fbfa8402a28dd2a53a37e67a83fd61"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:30.172996Z","signature_b64":"ycdsRxE8juN1RlIhAZVPNCdRjQbqs4vzrE69KW6sZH9rN+lJE7HT5sYgXQCCBhzg2tAz/JxiBhpOPXursKpfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef12ebcfc5c08273e10c64b250ebdae7f043292001c55014fb406389291d1714","last_reissued_at":"2026-05-18T01:19:30.172418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:30.172418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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