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Our main result states that every complete parallel submanifold of $\\rmG^+_2(\\R^{n+2})$\\,, which is not a curve, is contained in some totally geodesic submanifold as a symmetric submanifold. This result holds also if the ambient space is the non-compact dual of $\\rmG^+_2(\\R^{n+2})$\\,."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1107.5761","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-28T16:34:23Z","cross_cats_sorted":[],"title_canon_sha256":"7b31bfc30c505978770ba906550e4e640bfa8cf28dd5791f41847ce3c511c2d1","abstract_canon_sha256":"01705fa048ac781892cd45ee600fd831f500dcf8bc83b338ada1b8ba87a0722c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:51.304429Z","signature_b64":"pDDr3LmvTtJArS78oSk1NeQTF9l5TsSYJ4FG3JYLUXv+HL2m2qF95FR3CyVqYuQGsXSmnrmJ/2ePKEgJdQLYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10f85554164b62a512041f184e9d16165a2235478fee3c57087afb67fac1b79a","last_reissued_at":"2026-05-18T03:58:51.303826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:51.303826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parallel submanifolds of the real 2-Grassmannian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Tillmann Jentsch","submitted_at":"2011-07-28T16:34:23Z","abstract_excerpt":"A submanifold of a Riemannian symmetric space is called parallel if its second fundamental form is a parallel section of the appropriate tensor bundle. 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