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By theorems of \\'{A}lvarez L\\'{o}pez, our result implies that (M,F) is minimizable under the same conditions. As a corollary, we show that (M,F) is minimizable if F is of codimension 2 and the fundamental group of M is of polynomial growth."},"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":"0909.4508","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-24T17:53:20Z","cross_cats_sorted":[],"title_canon_sha256":"80402a6cf661252966c0424913e8b122a8fdcef66b89e5e7323671ce18a3f8c0","abstract_canon_sha256":"0738eef8b7e9787be4cc90d0b9a069cf7b8ef39a158688fc2d6d6aee10f183bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:25.249959Z","signature_b64":"gADhV43MGzo9NJC9jBslKXjVNOR6plFTB7dQgEcZe6gDuUI5aafll7b0q/XPZimXcoRSqFWFTNRrRuzMq9aCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08b1f6721d2ab0d774403e785923d5537ad419c71e9bb07c226b42f195ef9543","last_reissued_at":"2026-05-18T04:41:25.249364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:25.249364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimizability of developable Riemannian foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hiraku Nozawa","submitted_at":"2009-09-24T17:53:20Z","abstract_excerpt":"Let (M,F) be a closed manifold with a Riemannian foliation. 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