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We call a $C^1$-map $f:(M,H,g_H)\\to (N,h)$ into a Riemannian manifold $(N,h)$ a {\\em partial isometry} if the derivative map $df$ restricted to $H$ is isometric; in other words, $f^*h|_H=g_H$. The main result states that if $\\dim N>k$ then a smooth $H$-immersion $f_0:M\\to N$ satisfying $"},"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":"1009.5221","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-27T11:04:07Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"54a462c9b480eb0f896eb508f63db2d43c814a1e1b70c55b690487f2dd0ba766","abstract_canon_sha256":"2f7609b00e7cfb76ab9f946b3f04943a9782e593418c9ab968487cea9916ea77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:41.527940Z","signature_b64":"sjdhSzDyZfyy2o65yyfXFeA6Ex1WvcKPga5znDuocCbA0uTzoylaShu8L3MKLvHLW6xWIdaS/k8DThyBNH94Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e919b1dbd33c7819d144fd7f32fd6acb1b0f82a88be87a4e05050800cc624cb4","last_reissued_at":"2026-05-18T03:35:41.527493Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:41.527493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partial Isometries of a Sub-Riemannian Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Mahuya Datta","submitted_at":"2010-09-27T11:04:07Z","abstract_excerpt":"In this paper, we obtain the following generalisation of isometric $C^1$-immersion theorem of Nash and Kuiper. 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