{"id":"https://openalex.org/W4408126771","doi":"https://doi.org/10.3390/axioms14030190","title":"The Differential Geometry of a Space Curve via a Constant Vector in \u211d3","display_name":"The Differential Geometry of a Space Curve via a Constant Vector in \u211d3","publication_year":2025,"publication_date":"2025-03-04","ids":{"openalex":"https://openalex.org/W4408126771","doi":"https://doi.org/10.3390/axioms14030190"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14030190","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14030190","pdf_url":"https://www.mdpi.com/2075-1680/14/3/190/pdf?version=1741103153","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/2075-1680/14/3/190/pdf?version=1741103153","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053613182","display_name":"Azeb Alghanemi","orcid":"https://orcid.org/0000-0001-8778-1062"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Azeb Alghanemi","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116491439","display_name":"Ghadah Matar","orcid":null},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ghadah Matar","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073492723","display_name":"Amani Saloom","orcid":null},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Amani Saloom","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5053613182"],"corresponding_institution_ids":["https://openalex.org/I185163786"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.246,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.80102764,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"14","issue":"3","first_page":"190","last_page":"190"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9991000294685364,"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":0.9987999796867371,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9757000207901001,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"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":0.9031209945678711},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.7582944631576538},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.7048869132995605},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.6179884672164917},{"id":"https://openalex.org/keywords/differential-geometry-of-curves","display_name":"Differential geometry of curves","score":0.6084398031234741},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5962285995483398},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5716255307197571},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.5691545009613037},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5680758357048035},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5275484919548035},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45725104212760925},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4489986002445221},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.42346012592315674},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2943381667137146},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.22006487846374512},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1878359615802765},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15164422988891602},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.11608585715293884}],"concepts":[{"id":"https://openalex.org/C162546045","wikidata":"https://www.wikidata.org/wiki/Q947922","display_name":"Frenet\u2013Serret formulas","level":3,"score":0.9031209945678711},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.7582944631576538},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.7048869132995605},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.6179884672164917},{"id":"https://openalex.org/C194596105","wikidata":"https://www.wikidata.org/wiki/Q2254404","display_name":"Differential geometry of curves","level":5,"score":0.6084398031234741},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5962285995483398},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5716255307197571},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.5691545009613037},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5680758357048035},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5275484919548035},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45725104212760925},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4489986002445221},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.42346012592315674},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2943381667137146},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.22006487846374512},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1878359615802765},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15164422988891602},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.11608585715293884},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14030190","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14030190","pdf_url":"https://www.mdpi.com/2075-1680/14/3/190/pdf?version=1741103153","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:8831629b1edc46118611b077d386aece","is_oa":true,"landing_page_url":"https://doaj.org/article/8831629b1edc46118611b077d386aece","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 3, p 190 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14030190","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14030190","pdf_url":"https://www.mdpi.com/2075-1680/14/3/190/pdf?version=1741103153","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4408126771.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W91071685","https://openalex.org/W1984497978","https://openalex.org/W1995570756","https://openalex.org/W2021577575","https://openalex.org/W2028925500","https://openalex.org/W2065083610","https://openalex.org/W2092167646","https://openalex.org/W2118727875","https://openalex.org/W2139347315","https://openalex.org/W2322038588","https://openalex.org/W2526387968","https://openalex.org/W2527483937","https://openalex.org/W2552847845","https://openalex.org/W2789360120","https://openalex.org/W2908449575","https://openalex.org/W3005198801","https://openalex.org/W3168144548","https://openalex.org/W3206420412","https://openalex.org/W3215201346","https://openalex.org/W4213368568","https://openalex.org/W4243744369","https://openalex.org/W4382446884","https://openalex.org/W4400207852","https://openalex.org/W4401337803","https://openalex.org/W6603723405","https://openalex.org/W6657866388","https://openalex.org/W6728371968","https://openalex.org/W6791321741","https://openalex.org/W6802848686"],"related_works":["https://openalex.org/W4312987166","https://openalex.org/W228749424","https://openalex.org/W195196555","https://openalex.org/W4254546426","https://openalex.org/W2783731493","https://openalex.org/W2006374187","https://openalex.org/W156735263","https://openalex.org/W2741461870","https://openalex.org/W4299719436","https://openalex.org/W2952094119"],"abstract_inverted_index":{"The":[0,141],"differential":[1,37,70],"geometry":[2,38,71],"of":[3,10,39,47,59,72,81,97,104,113,156,174],"space":[4,40,61,75,98],"curves":[5,99],"is":[6,32,53,65,129],"a":[7,29,48,60,121,126,160],"fascinating":[8],"area":[9],"research":[11],"for":[12],"mathematicians":[13],"and":[14,16,63,78,94,144,149,162],"physicists,":[15],"this":[17,27,88,105,179],"refers":[18],"to":[19,34,67,151,171],"its":[20,145],"crucial":[21],"applications":[22],"in":[23,51,55,102,117,159,178],"many":[24],"areas.":[25],"In":[26],"paper,":[28],"new":[30,89,92,106,122,134,139,142],"method":[31],"derived":[33],"study":[35,68],"the":[36,44,56,69,73,95,110,138,153,175],"curves.":[41],"More":[42,108],"specifically,":[43,109],"position":[45,111,154],"vector":[46,50,155],"constant":[49],"R3":[52],"given":[54,74,86,116,170],"Frenet":[57],"apparatus":[58],"curve,":[62],"it":[64],"implemented":[66],"curve.":[76],"Easy":[77],"neat":[79],"proofs":[80],"various":[82],"well-known":[83],"results":[84,93,176],"are":[85,100,115,147,169],"using":[87],"method.":[90,107],"Also,":[91],"properties":[96],"obtained":[101,177],"light":[103],"vectors":[112],"helices":[114],"simple":[118,161],"forms.":[119],"Moreover,":[120],"frame":[123,143],"associated":[124,136],"with":[125,137],"smooth":[127],"curve":[128],"obtained,":[130],"as":[131,133],"well":[132],"curvatures":[135,146],"frame.":[140],"investigated":[148],"used":[150],"give":[152],"slant":[157],"helix":[158],"memorable":[163],"form.":[164],"Furthermore,":[165],"some":[166,173],"non-trivial":[167],"examples":[168],"illustrate":[172],"article.":[180]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2025-03-04T00:00:00"}
