{"paper":{"title":"Symmetries of projective spaces and spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Gy\\\"orgy P\\'al Geh\\'er","submitted_at":"2016-06-11T12:15:18Z","abstract_excerpt":"Let $H$ be either a complex inner product space of dimension at least two, or a real inner product space of dimension at least three. Let us fix an $\\alpha\\in \\left(0,\\tfrac{\\pi}{2}\\right)$. The purpose of this paper is to characterize all bijective transformations on the projective space $P(H)$ obtained from $H$ which preserves the angle $\\alpha$ between lines in both directions. (We emphasize that we do not assume anything about other angles). For real inner product spaces and when $H=\\mathbb{C}^2$ we do this for every $\\alpha$, and when $H$ is a complex inner product space of dimension at l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03584","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"}