{"id":"https://openalex.org/W4377107916","doi":"https://doi.org/10.3390/axioms12050486","title":"Quaternionic Shape Operator and Rotation Matrix on Ruled Surfaces","display_name":"Quaternionic Shape Operator and Rotation Matrix on Ruled Surfaces","publication_year":2023,"publication_date":"2023-05-17","ids":{"openalex":"https://openalex.org/W4377107916","doi":"https://doi.org/10.3390/axioms12050486"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12050486","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12050486","pdf_url":"https://www.mdpi.com/2075-1680/12/5/486/pdf?version=1684388639","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/5/486/pdf?version=1684388639","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100376055","display_name":"Yanlin Li","orcid":"https://orcid.org/0000-0003-1614-3228"},"institutions":[{"id":"https://openalex.org/I163151501","display_name":"Hangzhou Normal University","ror":"https://ror.org/014v1mr15","country_code":"CN","type":"education","lineage":["https://openalex.org/I163151501"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yanlin Li","raw_affiliation_strings":["Key Laboratory of Cryptography of Zhejiang Province, School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China"],"raw_orcid":"https://orcid.org/0000-0003-1614-3228","affiliations":[{"raw_affiliation_string":"Key Laboratory of Cryptography of Zhejiang Province, School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China","institution_ids":["https://openalex.org/I163151501"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005679944","display_name":"Abdussamet \u00c7al\u0131\u015fkan","orcid":"https://orcid.org/0000-0002-1512-2452"},"institutions":[{"id":"https://openalex.org/I64957398","display_name":"Ordu University","ror":"https://ror.org/04r0hn449","country_code":"TR","type":"education","lineage":["https://openalex.org/I64957398"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Abdussamet \u00c7al\u0131\u015fkan","raw_affiliation_strings":["Fatsa Vocational School, Accounting and Tax Applications, Ordu Universty, Ordu 52200, Turkey"],"raw_orcid":"https://orcid.org/0000-0002-1512-2452","affiliations":[{"raw_affiliation_string":"Fatsa Vocational School, Accounting and Tax Applications, Ordu Universty, Ordu 52200, Turkey","institution_ids":["https://openalex.org/I64957398"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100376055"],"corresponding_institution_ids":["https://openalex.org/I163151501"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":3.2222,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.91945802,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"12","issue":"5","first_page":"486","last_page":"486"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9984999895095825,"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/frenet\u2013serret-formulas","display_name":"Frenet\u2013Serret formulas","score":0.8986440896987915},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6938415765762329},{"id":"https://openalex.org/keywords/ruled-surface","display_name":"Ruled surface","score":0.6817041635513306},{"id":"https://openalex.org/keywords/rotation-matrix","display_name":"Rotation matrix","score":0.6613810062408447},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.621046781539917},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.5746833682060242},{"id":"https://openalex.org/keywords/gaussian-curvature","display_name":"Gaussian curvature","score":0.572604238986969},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5366958975791931},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.5345040559768677},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5193392038345337},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5041230916976929},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45456790924072266},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.44656896591186523},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.44502636790275574},{"id":"https://openalex.org/keywords/principal-curvature","display_name":"Principal curvature","score":0.44396719336509705},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4382185935974121},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.31731241941452026},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"Mean curvature","score":0.23266717791557312},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12374693155288696}],"concepts":[{"id":"https://openalex.org/C162546045","wikidata":"https://www.wikidata.org/wiki/Q947922","display_name":"Frenet\u2013Serret formulas","level":3,"score":0.8986440896987915},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6938415765762329},{"id":"https://openalex.org/C123635137","wikidata":"https://www.wikidata.org/wiki/Q840376","display_name":"Ruled surface","level":3,"score":0.6817041635513306},{"id":"https://openalex.org/C83633838","wikidata":"https://www.wikidata.org/wiki/Q1256564","display_name":"Rotation matrix","level":2,"score":0.6613810062408447},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.621046781539917},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5746833682060242},{"id":"https://openalex.org/C16140857","wikidata":"https://www.wikidata.org/wiki/Q945953","display_name":"Gaussian curvature","level":3,"score":0.572604238986969},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5366958975791931},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5345040559768677},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5193392038345337},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5041230916976929},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45456790924072266},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.44656896591186523},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.44502636790275574},{"id":"https://openalex.org/C16977076","wikidata":"https://www.wikidata.org/wiki/Q1589551","display_name":"Principal curvature","level":4,"score":0.44396719336509705},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4382185935974121},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.31731241941452026},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.23266717791557312},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12374693155288696},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12050486","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12050486","pdf_url":"https://www.mdpi.com/2075-1680/12/5/486/pdf?version=1684388639","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e1c1aa919a504e828d29defdb52e1ef3","is_oa":true,"landing_page_url":"https://doaj.org/article/e1c1aa919a504e828d29defdb52e1ef3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 5, p 486 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/5/486/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12050486","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 12; Issue 5; Pages: 486","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12050486","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12050486","pdf_url":"https://www.mdpi.com/2075-1680/12/5/486/pdf?version=1684388639","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G260937657","display_name":null,"funder_award_id":"12101168","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3468771053","display_name":null,"funder_award_id":"LQ22A010014","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5913933531","display_name":"\u5947\u70b9\u7406\u8bba\u5728\u5947\u5f02\u5b50\u6d41\u5f62\u548c\u62d3\u6251\u6570\u636e\u5206\u6790\u4e2d\u7684\u5e94\u7528","funder_award_id":"LQ22A010014","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"},{"id":"https://openalex.org/G841991167","display_name":null,"funder_award_id":"12101168","funder_id":"https://openalex.org/F4320338464","funder_display_name":"Natural Science Foundation of Zhejiang Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4377107916.pdf","grobid_xml":"https://content.openalex.org/works/W4377107916.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W6615101","https://openalex.org/W641005545","https://openalex.org/W873204051","https://openalex.org/W1192329422","https://openalex.org/W1494563177","https://openalex.org/W1527786550","https://openalex.org/W1618815127","https://openalex.org/W1964153994","https://openalex.org/W1985416560","https://openalex.org/W2002351086","https://openalex.org/W2006521751","https://openalex.org/W2010455397","https://openalex.org/W2011867188","https://openalex.org/W2019946977","https://openalex.org/W2020404331","https://openalex.org/W2026919502","https://openalex.org/W2028948041","https://openalex.org/W2121658301","https://openalex.org/W2132958298","https://openalex.org/W2147774191","https://openalex.org/W2159273968","https://openalex.org/W2207398646","https://openalex.org/W2489221431","https://openalex.org/W2516013396","https://openalex.org/W2530015822","https://openalex.org/W2560207568","https://openalex.org/W2599540157","https://openalex.org/W2749205738","https://openalex.org/W2774626843","https://openalex.org/W2782022515","https://openalex.org/W2809020561","https://openalex.org/W2917277782","https://openalex.org/W2942179845","https://openalex.org/W3004534868","https://openalex.org/W3009117363","https://openalex.org/W3016641873","https://openalex.org/W3023253965","https://openalex.org/W3044507056","https://openalex.org/W3159374643","https://openalex.org/W3193885405","https://openalex.org/W3197317813","https://openalex.org/W4235500832","https://openalex.org/W4281258330","https://openalex.org/W4294958094","https://openalex.org/W4296284611","https://openalex.org/W4306406252","https://openalex.org/W4312202504","https://openalex.org/W4312435947","https://openalex.org/W4312909758","https://openalex.org/W4313824547","https://openalex.org/W4315648692","https://openalex.org/W4317503052","https://openalex.org/W4322768285","https://openalex.org/W4365397491","https://openalex.org/W4366991569","https://openalex.org/W4382356244","https://openalex.org/W4393327046","https://openalex.org/W6653096275","https://openalex.org/W6688026798","https://openalex.org/W6748132703","https://openalex.org/W6775800090"],"related_works":["https://openalex.org/W3197589240","https://openalex.org/W4287773804","https://openalex.org/W3029707129","https://openalex.org/W4385582547","https://openalex.org/W1670292717","https://openalex.org/W4377107916","https://openalex.org/W2136497801","https://openalex.org/W1567144222","https://openalex.org/W1504899994","https://openalex.org/W4362673123"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,52],"examine":[4,53],"the":[5,14,18,22,27,30,40,45,54,61,72,88],"relationship":[6],"between":[7],"Darboux":[8,15],"frames":[9],"along":[10],"parameter":[11],"curves":[12],"and":[13,43,57,90],"frame":[16],"of":[17,21,29,60,74,78],"base":[19],"curve":[20],"ruled":[23,62],"surface.":[24,63],"We":[25,64,81],"derive":[26],"equations":[28],"quaternionic":[31],"shape":[32],"operators,":[33,51],"which":[34],"can":[35],"rotate":[36],"tangent":[37],"vectors":[38,76],"around":[39],"normal":[41],"vector,":[42],"find":[44],"corresponding":[46],"rotation":[47],"matrices.":[48],"Using":[49],"these":[50,67],"Gauss":[55],"curvature":[56,59],"mean":[58],"explore":[65],"how":[66],"properties":[68],"are":[69],"found":[70],"by":[71],"use":[73],"Frenet":[75],"instead":[77],"generator":[79],"vectors.":[80],"provide":[82],"illustrative":[83],"examples":[84],"to":[85],"better":[86],"demonstrate":[87],"concepts":[89],"results":[91],"discussed.":[92]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":16}],"updated_date":"2026-07-13T07:31:44.756512","created_date":"2025-10-10T00:00:00"}
