{"id":"https://openalex.org/W4254290936","doi":"https://doi.org/10.1007/978-3-319-91755-9_2","title":"Riemannian Metrics","display_name":"Riemannian Metrics","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W4254290936","doi":"https://doi.org/10.1007/978-3-319-91755-9_2"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-91755-9_2","doi":"https://doi.org/10.1007/978-3-319-91755-9_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-91755-9_2","pdf_url":null,"source":{"id":"https://openalex.org/S4210201401","display_name":"Graduate texts in mathematics","issn_l":"0072-5285","issn":["0072-5285","2197-5612"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graduate Texts in Mathematics","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W2896405912","display_name":"Introduction to Riemannian Manifolds"},"type":"book-chapter","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000331309","display_name":"John Michael Lee","orcid":"https://orcid.org/0000-0001-8473-4674","observed_orcids":["https://orcid.org/0000-0001-8473-4674"]},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John M. Lee","raw_affiliation_strings":["Department of Mathematics, University of Washington, Seattle, WA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Washington, Seattle, WA, USA","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000331309"],"corresponding_institution_ids":["https://openalex.org/I201448701"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.73947896,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"9","last_page":"54"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.005200000014156103,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11960","display_name":"Relativity and Gravitational Theory","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/riemannian-metrics","display_name":"Riemannian metrics","score":1.0},{"id":"https://openalex.org/keywords/pseudo-riemannian-metrics","display_name":"pseudo-Riemannian metrics","score":0.9649999737739563},{"id":"https://openalex.org/keywords/metric-construction","display_name":"metric construction","score":0.7279999852180481},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"differential geometry","score":0.7680000066757202},{"id":"https://openalex.org/keywords/tangent-space","display_name":"tangent space","score":0.4580000042915344},{"id":"https://openalex.org/keywords/inner-product","display_name":"inner product","score":0.35199999809265137}],"concepts":[{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.6683967709541321},{"id":"https://openalex.org/C4306028","wikidata":"https://www.wikidata.org/wiki/Q2185349","display_name":"Fundamental theorem of Riemannian geometry","level":4,"score":0.5464147925376892},{"id":"https://openalex.org/C129049296","wikidata":"https://www.wikidata.org/wiki/Q548675","display_name":"Levi-Civita connection","level":5,"score":0.49076685309410095},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48016849160194397},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4405291974544525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3912433087825775},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37486469745635986},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33307284116744995},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11347836256027222},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.1078844666481018},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-319-91755-9_2","doi":"https://doi.org/10.1007/978-3-319-91755-9_2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-91755-9_2","pdf_url":null,"source":{"id":"https://openalex.org/S4210201401","display_name":"Graduate texts in mathematics","issn_l":"0072-5285","issn":["0072-5285","2197-5612"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graduate Texts in Mathematics","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7097245724","https://openalex.org/W7100326213","https://openalex.org/W643777154","https://openalex.org/W4285192097","https://openalex.org/W3094083716","https://openalex.org/W1501351391","https://openalex.org/W177222413","https://openalex.org/W7020969640","https://openalex.org/W1555671175","https://openalex.org/W4320522074"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-10-10T09:11:00.788812","created_date":"2022-05-12T00:00:00"}