{"paper":{"title":"Projective Compactness and Conformal Boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andreas Cap, A. Rod Gover","submitted_at":"2014-06-17T03:17:29Z","abstract_excerpt":"Let $\\overline{M}$ be a smooth manifold with boundary $\\partial M$ and interior $M$. Consider an affine connection $\\nabla$ on $M$ for which the boundary is at infinity. Then $\\nabla$ is projectively compact of order $\\alpha$ if the projective structure defined by $\\nabla$ smoothly extends to all of $\\overline{M}$ in a specific way that depends on no particular choice of boundary defining function. Via the Levi--Civita connection, this concept applies to pseudo--Riemannian metrics on $M$. We study the relation between interior geometry and the possibilities for compactification, and then devel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4225","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"}