{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XIQVTCZA3WAPHIE2EBTUF2OL7F","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b2ab3b77355d76a5e1cd824461e05b9f01195510b0bfcacd34fc6a4d7275e36a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-18T16:49:13Z","title_canon_sha256":"6f05e27451869fff1d1ce746a8eb06384d14086cdd18060188b6467e3192a089"},"schema_version":"1.0","source":{"id":"1603.05916","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05916","created_at":"2026-05-18T00:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05916v1","created_at":"2026-05-18T00:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05916","created_at":"2026-05-18T00:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"XIQVTCZA3WAP","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XIQVTCZA3WAPHIE2","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XIQVTCZA","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:cfdaab91325973a02ea9e44f126b09e5d76aad89c42ec97f4ef3eeb0c8d042cd","target":"graph","created_at":"2026-05-18T00:39:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Given a compact manifold $M$ and a Riemannian manifold $N$ of bounded geometry, we consider the manifold ${\\rm Imm} (M,N)$ of immersions from $M$ to $N$ and its subset ${\\rm Imm}_\\mu (M,N)$ of those immersions with the property that the volume-form of the pull-back metric equals $\\mu$. We first show that the non-minimal elements of ${\\rm Imm}_\\mu (M,N) $ form a splitting submanifold. On this submanifold we consider the Levi-Civita connection for various natural Sobolev metrics write down the geodesic equation and show local well-posedness in many cases. The question is a natural generalization","authors_text":"Martin Bauer, Olaf M\\\"uller, Peter Michor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-18T16:49:13Z","title":"Riemannian geometry of the space of volume preserving immersions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05916","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:28e90482c8cfbb4b4949102e58f77791ea46e46a2bd079e5f5f14afaec65def3","target":"record","created_at":"2026-05-18T00:39:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b2ab3b77355d76a5e1cd824461e05b9f01195510b0bfcacd34fc6a4d7275e36a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-18T16:49:13Z","title_canon_sha256":"6f05e27451869fff1d1ce746a8eb06384d14086cdd18060188b6467e3192a089"},"schema_version":"1.0","source":{"id":"1603.05916","kind":"arxiv","version":1}},"canonical_sha256":"ba21598b20dd80f3a09a206742e9cbf971bf3edf142fb53c109594048d7d585c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba21598b20dd80f3a09a206742e9cbf971bf3edf142fb53c109594048d7d585c","first_computed_at":"2026-05-18T00:39:07.185142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:07.185142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dYf1OEsicGtWRwo3oRmwzWd77JvDeUf42tmQAdcYTYGHLZr8/9XRRxzohZhLErwEktST6jwsvJsDyu43pAmIDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:07.185889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05916","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28e90482c8cfbb4b4949102e58f77791ea46e46a2bd079e5f5f14afaec65def3","sha256:cfdaab91325973a02ea9e44f126b09e5d76aad89c42ec97f4ef3eeb0c8d042cd"],"state_sha256":"6e6bfaef60b2ea2f204ce853a7d24912ffe4eb386e3c8602e6f552499cc43ed5"}