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We note the local coordinates of g and q are circulant matrices. Their first orders are (A, B, C, B), A, B, C \\in FM and (0, 1, 0, 0), respectively.\n  Let \\nabla be the connection of g. Further, let mu_{1}, mu_{2},mu_{3}, mu_{4}, mu_{5}, mu_{6} be the sectional curvatures of 2-sections {x, qx}, {x, q^{2}x}, {q^{3}x, x}, {qx, q^{2}x}, {qx, q^{3}x}, {q^{2}x, q^{3}x} for arbitrary vector x in T_{p}M$, p is in M . Then we have that q^{4}=E; g(qx, qy)=g(x,y), x, y are in chiM.\n  The main results of the ","authors_text":"Dimitar Razpopov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-09T10:50:12Z","title":"On the geometry of four dimensional Riemannian manifold with a circulant metric and a circulant affinor structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1820","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7e0fc09b37f329f4934470451dd2f5ec74a0fccdbd92021e2ce53e41fb96c5c0","target":"record","created_at":"2026-05-18T01:17:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1a603c92b6d9c842395a0e095fd32ccb5fd91e77eabacae34f473bca8766c4ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-09T10:50:12Z","title_canon_sha256":"3260db249b80ea0f593d682fa4258e7133eda49d63ea65c6bfe32988b8c5440e"},"schema_version":"1.0","source":{"id":"1110.1820","kind":"arxiv","version":1}},"canonical_sha256":"f56ba9afd187ed5b7348e1954ad7fd9543ad46f0187579d3b44745928ed526c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f56ba9afd187ed5b7348e1954ad7fd9543ad46f0187579d3b44745928ed526c3","first_computed_at":"2026-05-18T01:17:01.583908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:01.583908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zOtTWIn5uL6D1yBx8iFDYxEiLK9Wysxz7v5NRtersy6ygmw+GyPEGjunUU9CAvf2IZ1SVbcLaJpxbprPq6//CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:01.584534Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1820","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e0fc09b37f329f4934470451dd2f5ec74a0fccdbd92021e2ce53e41fb96c5c0","sha256:2784961b6df5e76d48ba89d7e4d83c3080b2584a82e978141e6974b1510a0f8d"],"state_sha256":"7d810e16eae6af96bfa293432c500716f865e5092b6ee97c7ee0eba80df473cf"}