{"paper":{"title":"A perspective on totally geodesic submanifolds of the symmetric space $G_2/SO(4)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"C\\'andido Mart\\'in-Gonz\\'alez, Cristina Draper","submitted_at":"2025-04-10T09:28:50Z","abstract_excerpt":"We provide an independent proof of the classification of the maximal totally geodesic submanifolds of the symmetric spaces $G_2$ and $G_2/SO(4)$, jointly with very natural descriptions of all of these submanifolds. The description of the totally geodesic submanifolds of $G_2$ is in terms of (1) principal subalgebras of $\\mathfrak{g}_2$; (2) stabilizers of nonzero points of $\\mathbb{R}^7$; (3) stabilizers of associative subalgebras; (4) the set of order two elements in $G_2$ (and its translations). The space $G_2/SO(4)$ is identified with the set of associative subalgebras of $\\mathbb{R}^7$ and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.07586","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.07586/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"}