{"paper":{"title":"On the extendability of parallel sections of linear connections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antonio J. Di Scala, Gianni Manno","submitted_at":"2014-05-29T19:58:51Z","abstract_excerpt":"Let $\\pi:E\\to M$ be a vector bundle over a simply connected manifold and $\\nabla$ a linear connection in $\\pi$. Let $\\sigma: U \\rightarrow E$ be a $\\nabla$-parallel section of $\\pi$ defined on a connected open subset $U$ of $M$. We give sufficient conditions on $U$ in order to extend $\\sigma$ to the whole $M$. We mainly concentrate to the case when $M$ is a $2$-dimensional simply connected manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7688","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"}