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As an application, we mainly study the metric $F$ of weakly isotropic flag curvature ${\\bf K} = \\frac{3 \\theta}{F} + \\sigma$, where $\\theta=\\theta_i(x) y^i \\neq 0$ is a $1$-form and $\\sigma =\\sigma(x)$ is a scalar function. We prove that in this case, $F$ must be a Randers "},"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":"1503.00055","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-28T02:12:43Z","cross_cats_sorted":[],"title_canon_sha256":"2d63ff8b225cb0a6e533d6908afab59a11ceafb18130c87a1befff27737ffe11","abstract_canon_sha256":"f3d37055355e87f251266b941e9248be134e16e292782195bd4fbe7e50ec5833"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:18.079999Z","signature_b64":"/jLHjr6xIzpPTNDiqSMEBPlHoXUlQx10jDMdaa9rmBxG5J1VmLKdGVNDpKqEFX3cGnJlS7yim558VOEynryyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b94e47e41db041e3ddb65fd069c9092f4a947cb2b821c1c919a2d16248d3a459","last_reissued_at":"2026-05-18T00:30:18.079250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:18.079250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finsler metrics of weakly isotropic flag curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Benling Li","submitted_at":"2015-02-28T02:12:43Z","abstract_excerpt":"Finsler metrics of scalar flag curvature play an important role to show the complexity and richness of general Finsler metrics. In this paper, on an $n$-dimensional manifold $M$ we study the Finsler metric $F=F(x,y)$ of scalar flag curvature ${\\bf K} = {\\bf K}(x,y)$ and discover some equations ${\\bf K}$ should be satisfied. As an application, we mainly study the metric $F$ of weakly isotropic flag curvature ${\\bf K} = \\frac{3 \\theta}{F} + \\sigma$, where $\\theta=\\theta_i(x) y^i \\neq 0$ is a $1$-form and $\\sigma =\\sigma(x)$ is a scalar function. 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