{"paper":{"title":"Canonical connection on contact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Rui Wang, Yong-Geun Oh","submitted_at":"2012-12-19T20:24:58Z","abstract_excerpt":"We introduce a canonical affine connection on the contact manifold $(Q,\\xi)$, which is associated to each contact triad $(Q,\\lambda,J)$ where $\\lambda$ is a contact form and $J:\\xi \\to \\xi$ is an endomorphism with $J^2 = -id$ compatible to $d\\lambda$. We call it the \\emph{contact triad connection} of $(Q,\\lambda,J)$ and prove its existence and uniqueness. The connection is canonical in that the pull-back connection $\\phi^*\\nabla$ of a triad connection $\\nabla$ becomes the triad connection of the pull-back triad $(Q, \\phi^*\\lambda, \\phi^*J)$ for any diffeomorphism $\\phi:Q \\to Q$ satisfying $\\ph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4817","kind":"arxiv","version":3},"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"}