{"paper":{"title":"The Casimir operator of a metric connection with skew-symmetric torsion","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ilka Agricola, Thomas Friedrich (Berlin)","submitted_at":"2003-05-16T07:37:12Z","abstract_excerpt":"For any triple $(M^n, g, \\nabla)$ consisting of a Riemannian manifold and a metric connection with skew-symmetric torsion we introduce an elliptic, second order operator $\\Omega$ acting on spinor fields. In case of a reductive space and its canonical connection our construction yields the Casimir operator of the isometry group. Several non-homogeneous geometries (Sasakian, nearly K\\\"ahler, cocalibrated $\\mathrm{G}_2$-structures) admit unique connections with skew-symmetric torsion. We study the corresponding Casimir operator and compare its kernel with the space of $\\nabla$-parallel spinors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305233","kind":"arxiv","version":2},"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"}