{"id":"https://openalex.org/W4393394385","doi":"https://doi.org/10.3934/math.2024610","title":"Geometry of tubular surfaces and their focal surfaces in Euclidean 3-space","display_name":"Geometry of tubular surfaces and their focal surfaces in Euclidean 3-space","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4393394385","doi":"https://doi.org/10.3934/math.2024610"},"language":"en","primary_location":{"id":"doi:10.3934/math.2024610","doi":"https://doi.org/10.3934/math.2024610","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.2024610","pdf_url":"http://www.aimspress.com/aimspress-data/math/2024/5/PDF/math-09-05-610.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://www.aimspress.com/aimspress-data/math/2024/5/PDF/math-09-05-610.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062795470","display_name":"M. Khalifa Saad","orcid":"https://orcid.org/0000-0002-8516-4041","observed_orcids":["https://orcid.org/0000-0002-8516-4041"]},"institutions":[{"id":"https://openalex.org/I4210151290","display_name":"Islamic University of Madinah","ror":"https://ror.org/03rcp1y74","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210151290"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"M. Khalifa Saad","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Islamic University of Madinah, KSA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, KSA","institution_ids":["https://openalex.org/I4210151290"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063697880","display_name":"Nural Y\u00fcksel","orcid":"https://orcid.org/0000-0003-3360-5148","observed_orcids":["https://orcid.org/0000-0003-3360-5148"]},"institutions":[{"id":"https://openalex.org/I87673952","display_name":"Erciyes University","ror":"https://ror.org/047g8vk19","country_code":"TR","type":"education","lineage":["https://openalex.org/I87673952"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Nural Y\u00fcksel","raw_affiliation_strings":["Department of Mathematics, Erciyes University, 38039 Kayseri, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Erciyes University, 38039 Kayseri, Turkey","institution_ids":["https://openalex.org/I87673952"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092516656","display_name":"Nurdan O\u011fra\u015f","orcid":"https://orcid.org/0000-0002-5539-4890","observed_orcids":["https://orcid.org/0000-0002-5539-4890"]},"institutions":[{"id":"https://openalex.org/I87673952","display_name":"Erciyes University","ror":"https://ror.org/047g8vk19","country_code":"TR","type":"education","lineage":["https://openalex.org/I87673952"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Nurdan O\u011fra\u015f","raw_affiliation_strings":["Department of Mathematics, Erciyes University, 38039 Kayseri, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Erciyes University, 38039 Kayseri, Turkey","institution_ids":["https://openalex.org/I87673952"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093307535","display_name":"Fatemah Abdullah Alghamdi","orcid":"https://orcid.org/0000-0003-3774-6917","observed_orcids":["https://orcid.org/0000-0003-3774-6917","https://orcid.org/0000-0001-8760-762X"]},"institutions":[{"id":"https://openalex.org/I76571253","display_name":"Imam Abdulrahman Bin Faisal University","ror":"https://ror.org/038cy8j79","country_code":"SA","type":"education","lineage":["https://openalex.org/I76571253"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Fatemah Alghamdi","raw_affiliation_strings":["Financial Sciences Department, Applied College, Imam Abdulrahman Bin Faisal University, KSA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Financial Sciences Department, Applied College, Imam Abdulrahman Bin Faisal University, KSA","institution_ids":["https://openalex.org/I76571253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038379298","display_name":"Ali A. Abdel-Salam","orcid":"https://orcid.org/0009-0001-4253-6730","observed_orcids":["https://orcid.org/0009-0001-4253-6730"]},"institutions":[{"id":"https://openalex.org/I118590987","display_name":"Northern Border University","ror":"https://ror.org/03j9tzj20","country_code":"SA","type":"education","lineage":["https://openalex.org/I118590987"]},{"id":"https://openalex.org/I4210151290","display_name":"Islamic University of Madinah","ror":"https://ror.org/03rcp1y74","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210151290"]},{"id":"https://openalex.org/I76571253","display_name":"Imam Abdulrahman Bin Faisal University","ror":"https://ror.org/038cy8j79","country_code":"SA","type":"education","lineage":["https://openalex.org/I76571253"]},{"id":"https://openalex.org/I87673952","display_name":"Erciyes University","ror":"https://ror.org/047g8vk19","country_code":"TR","type":"education","lineage":["https://openalex.org/I87673952"]}],"countries":["SA","TR"],"is_corresponding":true,"raw_author_name":"A. A. Abdel-Salam","raw_affiliation_strings":["Department of Mathematics, Applied College, Northern Border University, Rafha, KSA","Department of Mathematics, Erciyes University, 38039 Kayseri, Turkey","Department of Mathematics, Faculty of Science, Islamic University of Madinah, KSA","Financial Sciences Department, Applied College, Imam Abdulrahman Bin Faisal University, KSA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Applied College, Northern Border University, Rafha, KSA","institution_ids":["https://openalex.org/I118590987"]},{"raw_affiliation_string":"Department of Mathematics, Erciyes University, 38039 Kayseri, Turkey","institution_ids":["https://openalex.org/I87673952"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, KSA","institution_ids":["https://openalex.org/I4210151290"]},{"raw_affiliation_string":"Financial Sciences Department, Applied College, Imam Abdulrahman Bin Faisal University, KSA","institution_ids":["https://openalex.org/I76571253"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5038379298"],"corresponding_institution_ids":["https://openalex.org/I118590987","https://openalex.org/I4210151290","https://openalex.org/I76571253","https://openalex.org/I87673952"],"apc_list":{"value":1200,"currency":"USD","value_usd":1200},"apc_paid":{"value":1200,"currency":"USD","value_usd":1200},"fwci":2.7827,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.89985596,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"9","issue":"5","first_page":"12479","last_page":"12493"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9994999766349792,"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":0.9994999766349792,"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":0.00039999998989515007,"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/T12504","display_name":"Mathematics and Applications","score":0.0,"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/tubular-surfaces","display_name":"tubular surfaces","score":1.0},{"id":"https://openalex.org/keywords/focal-surfaces","display_name":"focal surfaces","score":0.9959999918937683},{"id":"https://openalex.org/keywords/three-dimensional-euclidean-space","display_name":"three-dimensional Euclidean space","score":0.9049999713897705},{"id":"https://openalex.org/keywords/geometric-invariants","display_name":"geometric invariants","score":0.8510000109672546},{"id":"https://openalex.org/keywords/flat-surfaces","display_name":"flat surfaces","score":0.8529999852180481},{"id":"https://openalex.org/keywords/minimal-surfaces","display_name":"minimal surfaces","score":1.0},{"id":"https://openalex.org/keywords/weingarten-surfaces","display_name":"Weingarten surfaces","score":0.9980000257492065},{"id":"https://openalex.org/keywords/linear-weingarten-surfaces","display_name":"linear Weingarten surfaces","score":0.9309999942779541},{"id":"https://openalex.org/keywords/asymptotic-curves","display_name":"asymptotic curves","score":0.9940000176429749},{"id":"https://openalex.org/keywords/geodesic-curves","display_name":"geodesic curves","score":0.9909999966621399}],"concepts":[{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.6369968056678772},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5693148970603943},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4776785969734192},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4647706151008606},{"id":"https://openalex.org/C25653684","wikidata":"https://www.wikidata.org/wiki/Q207648","display_name":"Solid geometry","level":2,"score":0.43343526124954224},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.368918240070343},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32589128613471985},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2281513214111328},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19026300311088562},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3934/math.2024610","doi":"https://doi.org/10.3934/math.2024610","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.2024610","pdf_url":"http://www.aimspress.com/aimspress-data/math/2024/5/PDF/math-09-05-610.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},{"id":"doi:10.21203/rs.3.rs-3178515/v1","doi":"https://doi.org/10.21203/rs.3.rs-3178515/v1","is_oa":true,"landing_page_url":"http://dx.doi.org/10.21203/rs.3.rs-3178515/v1","pdf_url":"https://www.researchsquare.com/article/rs-3178515/latest.pdf","source":{"id":"https://openalex.org/S4306525896","display_name":"Research Square","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Research Square","raw_type":"posted-content"},{"id":"pmh:oai:doaj.org/article:a98dcc6bb62242eba90be690a83965c0","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/a98dcc6bb62242eba90be690a83965c0","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,"listed_in":[],"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":"AIMS Mathematics, Vol 9, Iss 5, Pp 12479-12493 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/math.2024610","doi":"https://doi.org/10.3934/math.2024610","is_oa":true,"landing_page_url":"https://doi.org/10.3934/math.2024610","pdf_url":"http://www.aimspress.com/aimspress-data/math/2024/5/PDF/math-09-05-610.pdf","source":{"id":"https://openalex.org/S4210179087","display_name":"AIMS Mathematics","issn_l":"2473-6988","issn":["2473-6988"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1","oarl","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AIMS Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320331150","display_name":"Islamic University of Madinah","ror":"https://ror.org/03rcp1y74"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4393394385.pdf","grobid_xml":"https://content.openalex.org/works/W4393394385.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W232012359","https://openalex.org/W1644996520","https://openalex.org/W1994351320","https://openalex.org/W2015489438","https://openalex.org/W2045855190","https://openalex.org/W2054030830","https://openalex.org/W2072969858","https://openalex.org/W2101765969","https://openalex.org/W2129837424","https://openalex.org/W2157638641","https://openalex.org/W2344339929","https://openalex.org/W2393244423","https://openalex.org/W2791925188","https://openalex.org/W2892932787","https://openalex.org/W2896151217","https://openalex.org/W2911730863","https://openalex.org/W2916322746","https://openalex.org/W2936622404","https://openalex.org/W3038421792","https://openalex.org/W3119635975","https://openalex.org/W3188328301","https://openalex.org/W4226304946","https://openalex.org/W4246660313","https://openalex.org/W4298106144"],"related_works":["https://openalex.org/W4385069006","https://openalex.org/W2896151217","https://openalex.org/W4285310277","https://openalex.org/W4308800419","https://openalex.org/W7124148933","https://openalex.org/W4407008834","https://openalex.org/W4393259640","https://openalex.org/W2167143832","https://openalex.org/W2883282434","https://openalex.org/W2462912753"],"abstract_inverted_index":{"In":[0],"this":[1],"study,":[2],"we":[3,33,76],"examined":[4],"the":[5,28,41,56,63],"focal":[6],"surfaces":[7,10,24,70],"of":[8,44,59,68,83],"tubular":[9],"in":[11,25],"Euclidean":[12],"3-space":[13],"$":[14],"E^{3}":[15],"$.":[16],"We":[17],"achieved":[18],"some":[19],"significant":[20],"results":[21],"for":[22],"these":[23,45,69],"accordance":[26],"with":[27],"modified":[29],"orthogonal":[30],"frame.":[31],"Additionally,":[32,62],"proposed":[34],"a":[35],"few":[36],"geometric":[37,42],"invariants":[38],"that":[39],"illustrated":[40],"characteristics":[43],"surfaces,":[46,54],"such":[47],"as":[48,80],"flat,":[49],"minimal,":[50],"Weingarten,":[51],"and":[52,65],"linear-Weingarten":[53],"using":[55],"traditional":[57],"methods":[58],"differential":[60],"geometry.":[61],"asymptotic":[64],"geodesic":[66],"curves":[67],"have":[71],"been":[72],"researched.":[73],"At":[74],"last,":[75],"presented":[77],"an":[78,81],"example":[79],"instance":[82],"use":[84],"to":[85],"validate":[86],"our":[87],"theoretical":[88],"findings.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2024-04-02T00:00:00"}