{"paper":{"title":"On affine connections in a Riemannian manifold with a circulant metric and two circulant affinor structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dimitar Razpopov, Iva Dokuzova","submitted_at":"2010-10-27T16:20:07Z","abstract_excerpt":"In the present paper it is considered a class V of 3-dimensional Riemannian manifolds M with a metric g and two affinor tensors q and S. It is defined another metric \\bar{g} in M. The local coordinates of all these tensors are circulant matrices. It is found:\n  1)\\ a relation between curvature tensors R and \\bar{R} of g and \\bar{g}, respectively;\n  2)\\ an identity of the curvature tensor R of g in the case when the curvature tensor \\bar{R} vanishes;\n  3)\\ a relation between the sectional curvature of a 2-section of the type \\{x, qx\\} and the scalar curvature of M."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5728","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}