{"paper":{"title":"Horizontal Holonomy for Affine Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.OC","authors_text":"Amina Mortada, Boutheina Hafassa, Petri Kokkonen, Yacine Chitour","submitted_at":"2014-11-02T08:46:54Z","abstract_excerpt":"In this paper, we consider a smooth connected finite-dimensional manifold $M$, an affine connection $\\nabla$ with holonomy group $H^{\\nabla}$ and $\\Delta$ a smooth completely non integrable distribution. We define the $\\Delta$-horizontal holonomy group $H^{\\;\\nabla}_\\Delta$ as the subgroup of $H^{\\nabla}$ obtained by $\\nabla$-parallel transporting frames only along loops tangent to $\\Delta$. We first set elementary properties of $H^{\\;\\nabla}_\\Delta$ and show how to study it using the rolling formalism (\\cite{ChitourKokkonen}). In particular, it is shown that $H^{\\;\\nabla}_\\Delta$ is a Lie gro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0226","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"}