{"paper":{"title":"A new $\\frac{1}{2}$-Ricci type formula on the spinor bundle and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ioannis Chrysikos","submitted_at":"2017-03-12T14:02:47Z","abstract_excerpt":"Consider a Riemannian spin manifold $(M^{n}, g)$ $(n\\geq 3)$ endowed with a non-trivial 3-form $T\\in\\Lambda^{3}T^{*}M$, such that $\\nabla^{c}T=0$, where $\\nabla^{c}:=\\nabla^{g}+\\frac{1}{2}T$ is the metric connection with skew-torsion $T$. In this note we introduce a generalized $\\frac{1}{2}$-Ricci type formula for the spinorial action of the Ricci endomorphism ${\\rm Ric}^{s}(X)$, induced by the one-parameter family of metric connections $\\nabla^{s}:=\\nabla^{g}+2sT$. This new identity extends a result described by Th. Friedrich and E. C. Kim, about the action of the Riemannian Ricci endomorphis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04121","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"}