{"paper":{"title":"On $(N(k),\\xi)$-semi-Riemannian manifolds: Semisymmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mukut Mani Tripathi, Punam Gupta","submitted_at":"2012-02-28T07:26:16Z","abstract_excerpt":"$(N(k),\\xi)$-semi-Riemannian manifolds are defined. Examples and properties of $(N(k),\\xi)$-semi-Riemannian manifolds are given. Some relations involving ${\\cal T}_{a}$-curvature tensor in $(N(k),\\xi)$-semi-Riemannian manifolds are proved. $\\xi $-${\\cal T}_{a}$-flat $(N(k),\\xi)$-semi-Riemannian manifolds are defined. It is proved that if $M$ is an $n$-dimensional $\\xi $-${\\cal T}_{a}$-flat $(N(k),\\xi)$-semi-Riemannian manifold, then it is $\\eta $-Einstein under an algebraic condition. We prove that a semi-Riemannian manifold, which is $T$-recurrent or $T$-symmetric, is always $T$-semisymmetric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6138","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"}