{"paper":{"title":"Equiaffine immersions and pseudo-Riemannian space forms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.SG"],"primary_cat":"math.DG","authors_text":"Nicholas Rungi","submitted_at":"2025-12-10T12:02:08Z","abstract_excerpt":"We introduce an explicit construction that produces immersions into the pseudosphere $\\mathbb{S}^{n,n+1}$ and the pseudohyperbolic space $\\mathbb{H}^{n+1,n}$ starting from equiaffine immersions in $\\mathbb{R}^{n+1}$, and conversely. We describe how these immersions interact with a para-Sasaki metric defined on $\\mathbb{H}^{n+1,n}$ via a principal $\\mathbb{R}$-bundle structure over a para-K\\\"ahler manifold $\\mathbb H_\\tau^n$, called the para-complex hyperbolic space. In the case where the immersion in $\\mathbb{R}^{n+1}$ is an $n$-dimensional hyperbolic affine sphere, we obtain spacelike maximal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.09569","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.09569/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}