{
"schema_version": 1,
"kind": "ConceptView",
"producer": "concept-view-1",
"concept_id": "urn:uuid:34f22db1-cc59-44be-9cd8-005c9cadb6ad",
"labels": {
"zh-CN": "黎曼联络",
"en": "Riemannian connection"
},
"alternative_labels": [],
"scope_note": "",
"identity_status": "active",
"identity_revision": "8a7025aa6a2a03440c0392735f19e5eaf0798e2dc0ccf8ba9bad31f88697f53a",
"occurrences": [
{
"concept_id": "urn:uuid:34f22db1-cc59-44be-9cd8-005c9cadb6ad",
"book_id": "szekeres",
"edition_id": "source-snapshot-bc3404156f6e",
"lang": "zh-CN",
"route": "zh/chapter-18/04-pseudo-riemannian-manifolds",
"anchor": "first-0dad657edfc9067c98b1-zh",
"chapter": "18",
"section": "18.4",
"offset": 8363,
"range": [
14901,
15147
],
"source_revision": "1bbb27130bf7d8d0ec56ab51f9406b00c7ca2b06919edbe1a20361105c5aba6d",
"source_category": "translation",
"review_status": "unreviewed",
"role": "occurrence",
"role_basis": {
"kind": "explicit-source-uuid-marker"
},
"label": "黎曼联络(Riemannian connection)",
"context": {
"range": [
14883,
15546
],
"quote": "这个联络称为由度量张量$g$所定义的黎曼联络(Riemannian connection)。一个不施加条件 (i) 的物理理论的有趣例子是爱因斯坦–嘉当理论，其中挠率表示自旋 [9]。条件 (ii) 具有以下推论。设$\\gamma$是一条具有切向量$X ( t ) = { \\dot { \\gamma } } ( t )$的曲线，并设$Y$和$Z$是沿$\\gamma _ { : }$平行移动的向量场，从而$D _ { X } Y = D _ { X } Z = 0$。由式 (18.18) 可知，它们的内积$g ( Y , Z )$沿该曲线为常数：",
"quote_sha256": "22ce2c9d2769fe86a0d5050e6fb4b1f27314261799489e752c4fdebb22cfbdfd",
"environment": null,
"excerpt_omitted": false
},
"parallel_readings": [
{
"route": "en/chapter-18/04-pseudo-riemannian-manifolds",
"lang": "en",
"source_category": "original_transcription",
"basis": "registered-book-edition-section-language-context; not-concept-equivalence"
}
],
"id": "occ-bbfd1ae41985f0484fb94d5e"
},
{
"concept_id": "urn:uuid:34f22db1-cc59-44be-9cd8-005c9cadb6ad",
"book_id": "szekeres",
"edition_id": "source-snapshot-bc3404156f6e",
"lang": "en",
"route": "en/chapter-18/04-pseudo-riemannian-manifolds",
"anchor": "first-0dad657edfc9067c98b1-en",
"chapter": "18",
"section": "18.4",
"offset": 10947,
"range": [
17013,
17253
],
"source_revision": "abe4ca4f42fe5272187e66105b690e8b9f1e858c2725731a33be8d30fbcf1939",
"source_category": "original_transcription",
"review_status": "unreviewed",
"role": "occurrence",
"role_basis": {
"kind": "explicit-source-uuid-marker"
},
"label": "Riemannian connection",
"context": {
"range": [
16983,
17950
],
"quote": "This connection is called the Riemannian connection defined by the metric tensor $g$. An interesting example of a physical theory that does not impose condition (i) is the Einstein– Cartan theory where torsion represents spin [9]. Condition (ii) has the following consequence. Let $\\gamma$ be a curve with tangent vector $X ( t ) = { \\dot { \\gamma } } ( t )$ , and let $Y$ and $Z$ be vector fields parallel transported along $\\gamma _ { : }$ , so that $D _ { X } Y = D _ { X } Z = 0$ . By Eq. (18.18) it follows that their inner product $g ( Y , Z )$ is constant along the curve:",
"quote_sha256": "8fa82aec138c13c336c94f01472f4466b65f6c8db29049346247a27aed2a9bd9",
"environment": null,
"excerpt_omitted": false
},
"parallel_readings": [
{
"route": "zh/chapter-18/04-pseudo-riemannian-manifolds",
"lang": "zh-CN",
"source_category": "translation",
"basis": "registered-book-edition-section-language-context; not-concept-equivalence"
}
],
"id": "occ-65ba0f8c1058ba02c0c60e22"
}
],
"registered_positions": [
{
"route": "en/chapter-18/04-pseudo-riemannian-manifolds",
"lang": "en",
"section": "18.4",
"signal": "term-mark",
"label": "Riemannian connection",
"english": "Riemannian connection",
"offset": 9715
},
{
"route": "zh/chapter-18/04-pseudo-riemannian-manifolds",
"lang": "zh-CN",
"section": "18.4",
"signal": "term-mark",
"label": "黎曼联络",
"english": "Riemannian connection",
"offset": 7131
}
],
"statements": [],
"resolved_references": [
{
"raw": "href=\"02-covariant-derivative-of-tensor-fields#equation-18-18\"",
"href": "02-covariant-derivative-of-tensor-fields#equation-18-18",
"range": [
15341,
15403
],
"relation": "references",
"target_route": "zh/chapter-18/02-covariant-derivative-of-tensor-fields",
"target_anchor": "equation-18-18",
"resolved": true,
"reason": null,
"source_revision": "1bbb27130bf7d8d0ec56ab51f9406b00c7ca2b06919edbe1a20361105c5aba6d",
"source_route": "zh/chapter-18/04-pseudo-riemannian-manifolds",
"occurrence_id": "occ-bbfd1ae41985f0484fb94d5e"
},
{
"raw": "href=\"02-covariant-derivative-of-tensor-fields#equation-18-18\"",
"href": "02-covariant-derivative-of-tensor-fields#equation-18-18",
"range": [
17694,
17756
],
"relation": "references",
"target_route": "en/chapter-18/02-covariant-derivative-of-tensor-fields",
"target_anchor": "equation-18-18",
"resolved": true,
"reason": null,
"source_revision": "abe4ca4f42fe5272187e66105b690e8b9f1e858c2725731a33be8d30fbcf1939",
"source_route": "en/chapter-18/04-pseudo-riemannian-manifolds",
"occurrence_id": "occ-65ba0f8c1058ba02c0c60e22"
}
],
"reading_order": [
"occ-bbfd1ae41985f0484fb94d5e",
"occ-65ba0f8c1058ba02c0c60e22"
],
"recorded_dependencies": [],
"reading_paths": [],
"coverage": {
"registered_positions": 2,
"located_occurrences": 2,
"whole_book_search_complete": false,
"registered_positions_truncated": false,
"independent_human_review_implied": false
},
"unresolved": [],
"base_revision": "266433c19524eba9f14aa4f27b74fba05ca1c7c51fdeb998c7580fb9f393d033",
"optional_enrichments": []
}