{"paper":{"title":"On the space of oriented geodesics of hyperbolic 3-space","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Brendan Guilfoyle, Nikos Georgiou","submitted_at":"2007-02-09T22:16:09Z","abstract_excerpt":"We construct a K\\\"ahler structure (${\\mathbb{J}},\\Omega,{\\mathbb{G}}$) on the space ${\\mathbb{L}}({\\mathbb{H}}^3)$ of oriented geodesics of hyperbolic 3-space ${\\mathbb{H}}^3$ and investigate its properties. We prove that (${\\mathbb{L}}({\\mathbb{H}}^3),{\\mathbb{J}})$ is biholomorphic to ${\\mathbb{P}}^1\\times{\\mathbb{P}}^1-\\bar{\\Delta}$, where $\\bar{\\Delta}$ is the reflected diagonal, and that the K\\\"ahler metric ${\\mathbb{G}}$ is of neutral signature, conformally flat and scalar flat. We establish that the identity component of the isometry group of the metric ${\\mathbb{G}}$ on ${\\mathbb{L}}({"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702276","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"}