{"paper":{"title":"Distribution of holonomy about closed geodesics in a product of hyperbolic planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Dubi Kelmer","submitted_at":"2009-11-02T14:58:59Z","abstract_excerpt":"Let $\\calM=\\Gamma\\bs \\calH^{(n)}$, where $\\calH^{(n)}$ is a product of $n+1$ hyperbolic planes and $\\Gamma\\subset\\PSL(2,\\bbR)^{n+1}$ is an irreducible cocompact lattice. We consider closed geodesics on $\\calM$ that propagate locally only in one factor. We show that, as the length tends to infinity, the holonomy rotations attached to these geodesics become equidistributed in $\\PSO(2)^n$ with respect to a certain measure. For the special case of lattices derived from quaternion algebras, we can give another interpretation of the holonomy angles under which this measure arises naturally."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0329","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"}