{"id":"https://openalex.org/W4382310385","doi":"https://doi.org/10.3390/sym15051077","title":"Two Special Types of Curves in Lorentzian \u03b1-Sasakian 3-Manifolds","display_name":"Two Special Types of Curves in Lorentzian \u03b1-Sasakian 3-Manifolds","publication_year":2023,"publication_date":"2023-05-12","ids":{"openalex":"https://openalex.org/W4382310385","doi":"https://doi.org/10.3390/sym15051077"},"language":"en","primary_location":{"id":"doi:10.3390/sym15051077","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051077","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1077/pdf?version=1684075477","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/5/1077/pdf?version=1684075477","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050211816","display_name":"Xiawei Chen","orcid":"https://orcid.org/0000-0002-8687-7932"},"institutions":[{"id":"https://openalex.org/I4210116828","display_name":"Mudanjiang Normal University","ror":"https://ror.org/02dzkdp68","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210116828"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiawei Chen","raw_affiliation_strings":["School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, China"],"raw_orcid":"https://orcid.org/0000-0002-8687-7932","affiliations":[{"raw_affiliation_string":"School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, China","institution_ids":["https://openalex.org/I4210116828"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045690411","display_name":"Haiming Liu","orcid":"https://orcid.org/0000-0002-0410-5980"},"institutions":[{"id":"https://openalex.org/I4210116828","display_name":"Mudanjiang Normal University","ror":"https://ror.org/02dzkdp68","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210116828"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haiming Liu","raw_affiliation_strings":["School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, China"],"raw_orcid":"https://orcid.org/0000-0002-0410-5980","affiliations":[{"raw_affiliation_string":"School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, China","institution_ids":["https://openalex.org/I4210116828"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045690411"],"corresponding_institution_ids":["https://openalex.org/I4210116828"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.5023,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55511699,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"15","issue":"5","first_page":"1077","last_page":"1077"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9998000264167786,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9998000264167786,"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/T12351","display_name":"Geometry and complex manifolds","score":0.9897000193595886,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9595000147819519,"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/frenet\u2013serret-formulas","display_name":"Frenet\u2013Serret formulas","score":0.5701270699501038},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5249485969543457},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4787523150444031},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38068026304244995},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.37664127349853516},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3374565839767456},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.311302125453949}],"concepts":[{"id":"https://openalex.org/C162546045","wikidata":"https://www.wikidata.org/wiki/Q947922","display_name":"Frenet\u2013Serret formulas","level":3,"score":0.5701270699501038},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5249485969543457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4787523150444031},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38068026304244995},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37664127349853516},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3374565839767456},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.311302125453949}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15051077","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051077","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1077/pdf?version=1684075477","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:68920021325149e89c07a05ef71174ea","is_oa":false,"landing_page_url":"https://doaj.org/article/68920021325149e89c07a05ef71174ea","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 5, p 1077 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/5/1077/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15051077","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":"Symmetry; Volume 15; Issue 5; Pages: 1077","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15051077","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15051077","pdf_url":"https://www.mdpi.com/2073-8994/15/5/1077/pdf?version=1684075477","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2886427685","display_name":null,"funder_award_id":"LH2021A020","funder_id":"https://openalex.org/F4320323085","funder_display_name":"Natural Science Foundation of Heilongjiang Province"},{"id":"https://openalex.org/G8133807199","display_name":null,"funder_award_id":"GP2022006","funder_id":"https://openalex.org/F4320327406","funder_display_name":"Mudanjiang Normal University"},{"id":"https://openalex.org/G8988797048","display_name":null,"funder_award_id":"ZYQN2019071","funder_id":"https://openalex.org/F4320327406","funder_display_name":"Mudanjiang Normal University"}],"funders":[{"id":"https://openalex.org/F4320323085","display_name":"Natural Science Foundation of Heilongjiang Province","ror":null},{"id":"https://openalex.org/F4320327406","display_name":"Mudanjiang Normal University","ror":"https://ror.org/02dzkdp68"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4382310385.pdf"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W1564103667","https://openalex.org/W1582894873","https://openalex.org/W1669319399","https://openalex.org/W1972365171","https://openalex.org/W1997335371","https://openalex.org/W2027099252","https://openalex.org/W2042423607","https://openalex.org/W2052714027","https://openalex.org/W2067663655","https://openalex.org/W2125793746","https://openalex.org/W2626300442","https://openalex.org/W2950289842","https://openalex.org/W2964220368","https://openalex.org/W2997162525","https://openalex.org/W3190171603","https://openalex.org/W3193885405","https://openalex.org/W3206453841","https://openalex.org/W4220682690","https://openalex.org/W4230839756","https://openalex.org/W4250863395","https://openalex.org/W4306701488","https://openalex.org/W4309013273","https://openalex.org/W4312202504","https://openalex.org/W4312435947","https://openalex.org/W4312909758","https://openalex.org/W4312934976","https://openalex.org/W4313824547","https://openalex.org/W4317503052","https://openalex.org/W4322768285","https://openalex.org/W4365397491","https://openalex.org/W4366991569","https://openalex.org/W6633782391","https://openalex.org/W6812479197","https://openalex.org/W6849920934","https://openalex.org/W6986926221"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2609788161","https://openalex.org/W2890994448","https://openalex.org/W4312766700","https://openalex.org/W1967787111","https://openalex.org/W2998181671","https://openalex.org/W2361423042","https://openalex.org/W2075234962","https://openalex.org/W4308279019","https://openalex.org/W1995601874"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,30,47,71,101],"focus":[4],"on":[5],"the":[6,11,32,39,42,49,53,58,66,73,76,82,90,95,107,111,119],"research":[7],"and":[8,14,19,44,55,61,87,114],"analysis":[9],"of":[10,16,34,41,57,75,94,110],"geometric":[12,108],"properties":[13,109],"symmetry":[15],"slant":[17,59,91,112],"curves":[18,22],"contact":[20,62,77,97,115],"magnetic":[21,63,78,98,116],"in":[23,65,118],"Lorentzian":[24,35,67,85,120],"\u03b1-Sasakian":[25,68,86,121],"3-manifolds.":[26,69,122],"To":[27],"do":[28],"this,":[29],"define":[31],"notion":[33],"cross":[36],"product.":[37],"From":[38],"perspectives":[40],"Legendre":[43],"non-geodesic":[45],"curves,":[46],"found":[48,102],"ratio":[50],"relationship":[51],"between":[52],"curvature":[54],"torsion":[56],"curve":[60,64,79,92,113,117],"Moreover,":[70],"utilized":[72],"property":[74],"to":[80,88,105],"characterize":[81],"manifold":[83],"as":[84],"find":[89],"type":[93],"Frenet":[96],"curve.":[99],"Furthermore,":[100],"an":[103],"example":[104],"verify":[106]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2023-06-28T00:00:00"}