{"paper":{"title":"On the Geometry of Flat Pseudo-Riemannian Homogeneous Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Wolfgang Globke","submitted_at":"2012-11-06T05:05:07Z","abstract_excerpt":"Let $M$ be complete flat pseudo-Riemannian homogeneous manifold and $\\Gamma\\subset\\Iso(\\RR^n_s)$ its fundamental group. We show that $M$ is a trivial fiber bundle $G/\\Gamma\\to M\\to\\RR^{n-k}$, where $G$ is the Zariski closure of $\\Gamma$ in $\\Iso(\\RR^n_s)$. Moreover, we show that the $G$-orbits in $\\RR^n_s$ are affinely diffeomorphic to $G$ endowed with the (0)-connection. If the induced metric on the $G$-orbits is non-degenerate, then $G$ (and hence $\\Gamma$) has linear abelian holonomy. If additionally $G$ is not abelian, then $G$ contains a certain subgroup of dimension 6. In particular, for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1111","kind":"arxiv","version":5},"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"}