{"id":"https://openalex.org/W1601457938","doi":"https://doi.org/10.1007/11499251_17","title":"Intrinsic Differential Geometry with Geometric Calculus","display_name":"Intrinsic Differential Geometry with Geometric Calculus","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1601457938","doi":"https://doi.org/10.1007/11499251_17","mag":"1601457938"},"language":"en","primary_location":{"id":"doi:10.1007/11499251_17","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11499251_17","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5100402176","display_name":"Hongbo Li","orcid":"https://orcid.org/0000-0003-1498-4285"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongbo Li","raw_affiliation_strings":["Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China","Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China#TAB#","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067361048","display_name":"Lina Cao","orcid":"https://orcid.org/0000-0002-7128-2450"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lina Cao","raw_affiliation_strings":["Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China","Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China#TAB#","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074748790","display_name":"Nanbin Cao","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nanbin Cao","raw_affiliation_strings":["Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China","Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China#TAB#","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074356526","display_name":"Weikun Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weikun Sun","raw_affiliation_strings":["Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China","Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Mathematics Mechanization Key Laboratory, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R. China#TAB#","institution_ids":["https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15366146,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"207","last_page":"216"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/differential-algebraic-geometry","display_name":"Differential algebraic geometry","score":0.6720007061958313},{"id":"https://openalex.org/keywords/covariant-derivative","display_name":"Covariant derivative","score":0.6572712063789368},{"id":"https://openalex.org/keywords/covariant-transformation","display_name":"Covariant transformation","score":0.6311612725257874},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.5894315838813782},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5331344604492188},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5110853910446167},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5033435225486755},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.4935206174850464},{"id":"https://openalex.org/keywords/affine-connection","display_name":"Affine connection","score":0.47567930817604065},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.44016560912132263},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4331130385398865},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4311661720275879},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4186001420021057},{"id":"https://openalex.org/keywords/differential-calculus","display_name":"Differential calculus","score":0.4109051823616028},{"id":"https://openalex.org/keywords/affine-geometry","display_name":"Affine geometry","score":0.4105231761932373},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3423653841018677},{"id":"https://openalex.org/keywords/affine-space","display_name":"Affine space","score":0.3313800096511841},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3223245143890381},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.19773295521736145},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14078426361083984},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.12319299578666687}],"concepts":[{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.6720007061958313},{"id":"https://openalex.org/C19492387","wikidata":"https://www.wikidata.org/wiki/Q2287715","display_name":"Covariant derivative","level":2,"score":0.6572712063789368},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.6311612725257874},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.5894315838813782},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5331344604492188},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5110853910446167},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5033435225486755},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4935206174850464},{"id":"https://openalex.org/C105561566","wikidata":"https://www.wikidata.org/wiki/Q1371213","display_name":"Affine connection","level":3,"score":0.47567930817604065},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.44016560912132263},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4331130385398865},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4311661720275879},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4186001420021057},{"id":"https://openalex.org/C56802139","wikidata":"https://www.wikidata.org/wiki/Q149999","display_name":"Differential calculus","level":2,"score":0.4109051823616028},{"id":"https://openalex.org/C23684344","wikidata":"https://www.wikidata.org/wiki/Q382520","display_name":"Affine geometry","level":4,"score":0.4105231761932373},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3423653841018677},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.3313800096511841},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3223245143890381},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.19773295521736145},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14078426361083984},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.12319299578666687},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/11499251_17","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11499251_17","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W122875470","https://openalex.org/W604279754","https://openalex.org/W2332193196","https://openalex.org/W2362124829","https://openalex.org/W3039357072","https://openalex.org/W3140595534","https://openalex.org/W4388254843"],"related_works":["https://openalex.org/W3128259744","https://openalex.org/W947039943","https://openalex.org/W2312953745","https://openalex.org/W1972070698","https://openalex.org/W3105987634","https://openalex.org/W2076532518","https://openalex.org/W1994982984","https://openalex.org/W3097223583","https://openalex.org/W1962273697","https://openalex.org/W2460584804"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
