{"id":"https://openalex.org/W2026892575","doi":"https://doi.org/10.1016/s0079-8169(08)x6065-9","title":"An Introduction to Differentiable Manifolds and Riemannian Geometry","display_name":"An Introduction to Differentiable Manifolds and Riemannian Geometry","publication_year":1975,"publication_date":"1975-01-01","ids":{"openalex":"https://openalex.org/W2026892575","doi":"https://doi.org/10.1016/s0079-8169(08)x6065-9","mag":"2026892575"},"language":"en","primary_location":{"id":"doi:10.1016/s0079-8169(08)x6065-9","doi":"https://doi.org/10.1016/s0079-8169(08)x6065-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0079-8169(08)x6065-9","pdf_url":null,"source":{"id":"https://openalex.org/S52343387","display_name":"Pure and applied mathematics","issn_l":"0079-8169","issn":["0079-8169","2162-3481"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pure and Applied Mathematics","raw_type":"book"},"parent_works":[],"lineage":["https://openalex.org/W2026892575"],"child_works_count":14,"type":"book","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.3716,"has_fulltext":false,"cited_by_count":1770,"citation_normalized_percentile":{"value":0.94936709,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9833999872207642,"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":0.9833999872207642,"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":0.014100000262260437,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.0006000000284984708,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/smooth-manifolds","display_name":"smooth manifolds","score":0.9700000286102295},{"id":"https://openalex.org/keywords/riemannian-geometry","display_name":"Riemannian geometry","score":0.9990000128746033},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"differential geometry","score":0.4880000054836273},{"id":"https://openalex.org/keywords/line-integrals","display_name":"line integrals","score":0.6510000228881836},{"id":"https://openalex.org/keywords/surface-integrals","display_name":"surface integrals","score":1.0},{"id":"https://openalex.org/keywords/divergence-and-curl","display_name":"divergence and curl","score":0.7770000100135803},{"id":"https://openalex.org/keywords/stokes-theorem","display_name":"Stokes' theorem","score":0.9729999899864197},{"id":"https://openalex.org/keywords/green-s-theorem","display_name":"Green's theorem","score":0.9959999918937683},{"id":"https://openalex.org/keywords/great-circle-arcs","display_name":"great circle arcs","score":0.7170000076293945}],"concepts":[{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.8224626779556274},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7121426463127136},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6813837885856628},{"id":"https://openalex.org/C146674193","wikidata":"https://www.wikidata.org/wiki/Q40139","display_name":"Curvature of Riemannian manifolds","level":5,"score":0.6560684442520142},{"id":"https://openalex.org/C4306028","wikidata":"https://www.wikidata.org/wiki/Q2185349","display_name":"Fundamental theorem of Riemannian geometry","level":4,"score":0.5135385990142822},{"id":"https://openalex.org/C516171914","wikidata":"https://www.wikidata.org/wiki/Q1224402","display_name":"Differential topology","level":5,"score":0.4860704243183136},{"id":"https://openalex.org/C82978714","wikidata":"https://www.wikidata.org/wiki/Q4394657","display_name":"Riemannian submersion","level":5,"score":0.4802287220954895},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4729352295398712},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4476453959941864},{"id":"https://openalex.org/C203934109","wikidata":"https://www.wikidata.org/wiki/Q7322952","display_name":"Ricci-flat manifold","level":4,"score":0.4208199381828308},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.3758416175842285},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.23354244232177734},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.09998077154159546}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0079-8169(08)x6065-9","doi":"https://doi.org/10.1016/s0079-8169(08)x6065-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0079-8169(08)x6065-9","pdf_url":null,"source":{"id":"https://openalex.org/S52343387","display_name":"Pure and applied mathematics","issn_l":"0079-8169","issn":["0079-8169","2162-3481"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pure and Applied Mathematics","raw_type":"book"}],"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/W4299300227","https://openalex.org/W7132819848","https://openalex.org/W2038151469","https://openalex.org/W1580579642","https://openalex.org/W1794104651","https://openalex.org/W6967746911","https://openalex.org/W176209861","https://openalex.org/W4310830429","https://openalex.org/W2975246077","https://openalex.org/W137189985"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":33},{"year":2021,"cited_by_count":43},{"year":2020,"cited_by_count":99},{"year":2019,"cited_by_count":78},{"year":2018,"cited_by_count":49},{"year":2017,"cited_by_count":43},{"year":2016,"cited_by_count":54},{"year":2015,"cited_by_count":38},{"year":2014,"cited_by_count":50},{"year":2013,"cited_by_count":56},{"year":2012,"cited_by_count":84}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2016-06-24T00:00:00"}
