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The metrics constructed by shrinking the fibers in this way can be interpreted as metrics obtained from a Cheeger deformation and are thus well known to be nonnegatively curved. On the other hand, if the fibers are homothetically enlarged, it depends on the triple of groups $(H,K,G)$ whether nonnegative curvature is maintained for small deformations.\n  Building on the "},"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":"1201.4744","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-23T15:42:52Z","cross_cats_sorted":[],"title_canon_sha256":"bad05d3bd61a8dec5104e37989f9e3fdfce73298b8294348f49c9c62163b3915","abstract_canon_sha256":"6850944010fe49f2cee456b6468df2617b19fbe1ffbf7c631e1716526a96bf60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:10.893364Z","signature_b64":"i6ZQcXOO1f8pWEE3T3NT1E9njEzjT651Fw1Hu6qdr4/QTtA9PzCG6DA84S2X7LLfp8YUE3y3lZ01O9F2gmU8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a3bce586e2f084942834e046464ba2a1affd5020974add2b99d6ede520242d3","last_reissued_at":"2026-05-18T03:41:10.892716Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:10.892716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonnegatively curved homogeneous metrics in low dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andreas Kollross, Megan M. Kerr","submitted_at":"2012-01-23T15:42:52Z","abstract_excerpt":"We consider invariant Riemannian metrics on compact homogeneous spaces $G/H$ where an intermediate subgroup $K$ between $G$ and $H$ exists. In this case, the homogeneous space $G/H$ is the total space of a Riemannian submersion. The metrics constructed by shrinking the fibers in this way can be interpreted as metrics obtained from a Cheeger deformation and are thus well known to be nonnegatively curved. 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