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As an application we show (Corollary 3) that every Berwald projectively flat metric is a Minkowski metric; this statement is a \"Berwald\" version of Hilbert's 4th problem.\n  Further, we investigate geodesic equivalence of Berwald metrics. Theorem 2 gives a system of PDE that has a (nontrivial) solution if and only if the given essentially Berwald metric admits a Riemannian metric that "},"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":"0811.0031","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-31T22:23:17Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"f5a3b4b053281a9e4767201cc49a686092662164eb37ace3e8839b001d4ba0e4","abstract_canon_sha256":"68c8157dac28b51de7a0d86720208f67ee6059175b8a14d18d697a25310bc3ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:06.850982Z","signature_b64":"wEdFTl8Qs3wKhSGwZZWGjYYEJXjymi0Ccx6dYoJLb7KX8hqUiNW7MUBSlvnlGsYJ56QNpamPNgUdZNmsKn16CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77197c279a3cdb789876ace804588a8fd7472e68a2f79d38667830f5f9bbf4c1","last_reissued_at":"2026-05-18T04:15:06.850485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:06.850485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Riemannian metrics having common geodesics with Berwald metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Vladimir S. 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