{"id":"https://openalex.org/W4210581943","doi":"https://doi.org/10.3390/axioms11020059","title":"Pythagorean Isoparametric Hypersurfaces in Riemannian and Lorentzian Space Forms","display_name":"Pythagorean Isoparametric Hypersurfaces in Riemannian and Lorentzian Space Forms","publication_year":2022,"publication_date":"2022-01-30","ids":{"openalex":"https://openalex.org/W4210581943","doi":"https://doi.org/10.3390/axioms11020059"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11020059","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11020059","pdf_url":"https://www.mdpi.com/2075-1680/11/2/59/pdf?version=1644549583","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/2075-1680/11/2/59/pdf?version=1644549583","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011931138","display_name":"Muhittin Evren Ayd\u0131n","orcid":"https://orcid.org/0000-0001-9337-8165"},"institutions":[{"id":"https://openalex.org/I143396566","display_name":"F\u0131rat University","ror":"https://ror.org/05teb7b63","country_code":"TR","type":"education","lineage":["https://openalex.org/I143396566"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Muhittin Evren Ayd\u0131n","raw_affiliation_strings":["Department of Mathematics, Firat University, Elazig 23119, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Firat University, Elazig 23119, Turkey","institution_ids":["https://openalex.org/I143396566"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070714097","display_name":"Adela Mihai","orcid":"https://orcid.org/0000-0003-2033-8394"},"institutions":[{"id":"https://openalex.org/I3123573182","display_name":"Transylvania University of Bra\u0219ov","ror":"https://ror.org/01cg9ws23","country_code":"RO","type":"education","lineage":["https://openalex.org/I3123573182"]},{"id":"https://openalex.org/I148178115","display_name":"Technical University of Civil Engineering of Bucharest","ror":"https://ror.org/03d187f57","country_code":"RO","type":"education","lineage":["https://openalex.org/I148178115"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Adela Mihai","raw_affiliation_strings":["Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania","Interdisciplinary Doctoral School, Transilvania University of Bra\u015fov, 500036 Bra\u015fov, Romania"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania","institution_ids":["https://openalex.org/I148178115"]},{"raw_affiliation_string":"Interdisciplinary Doctoral School, Transilvania University of Bra\u015fov, 500036 Bra\u015fov, Romania","institution_ids":["https://openalex.org/I3123573182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044302232","display_name":"C\u0131han \u00d6zg\u00fcr","orcid":"https://orcid.org/0000-0002-4579-7151"},"institutions":[{"id":"https://openalex.org/I4387154896","display_name":"\u0130zmir Demokrasi \u00dcniversitesi","ror":"https://ror.org/04c152q53","country_code":null,"type":"education","lineage":["https://openalex.org/I4387154896"]},{"id":"https://openalex.org/I132257509","display_name":"Izmir University","ror":"https://ror.org/013h3xr51","country_code":"TR","type":"education","lineage":["https://openalex.org/I132257509"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Cihan \u00d6zg\u00fcr","raw_affiliation_strings":["Department of Mathematics, \u0130zmir Democracy University, \u0130zmir 35140, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, \u0130zmir Democracy University, \u0130zmir 35140, Turkey","institution_ids":["https://openalex.org/I4387154896","https://openalex.org/I132257509"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070714097"],"corresponding_institution_ids":["https://openalex.org/I148178115","https://openalex.org/I3123573182"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.568,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.80210221,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"11","issue":"2","first_page":"59","last_page":"59"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9722999930381775,"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/T12504","display_name":"Mathematics and Applications","score":0.9722999930381775,"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/hypersurface","display_name":"Hypersurface","score":0.9434407353401184},{"id":"https://openalex.org/keywords/pythagorean-theorem","display_name":"Pythagorean theorem","score":0.8613988161087036},{"id":"https://openalex.org/keywords/sectional-curvature","display_name":"Sectional curvature","score":0.7545509338378906},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6402910947799683},{"id":"https://openalex.org/keywords/space-form","display_name":"Space form","score":0.6034905910491943},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5031408667564392},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.4865986108779907},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.47904908657073975},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47458481788635254},{"id":"https://openalex.org/keywords/pythagorean-triple","display_name":"Pythagorean triple","score":0.45075154304504395},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"Mean curvature","score":0.4347359538078308},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23804715275764465},{"id":"https://openalex.org/keywords/submanifold","display_name":"Submanifold","score":0.17708882689476013},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.17647528648376465},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07450807094573975}],"concepts":[{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.9434407353401184},{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.8613988161087036},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.7545509338378906},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6402910947799683},{"id":"https://openalex.org/C2776341046","wikidata":"https://www.wikidata.org/wiki/Q4381552","display_name":"Space form","level":3,"score":0.6034905910491943},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5031408667564392},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4865986108779907},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47904908657073975},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47458481788635254},{"id":"https://openalex.org/C80918210","wikidata":"https://www.wikidata.org/wiki/Q208225","display_name":"Pythagorean triple","level":3,"score":0.45075154304504395},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.4347359538078308},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23804715275764465},{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.17708882689476013},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.17647528648376465},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07450807094573975},{"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:10.3390/axioms11020059","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11020059","pdf_url":"https://www.mdpi.com/2075-1680/11/2/59/pdf?version=1644549583","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:5f829a1c75784a8bb5a062be41d8814d","is_oa":true,"landing_page_url":"https://doaj.org/article/5f829a1c75784a8bb5a062be41d8814d","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 11, Iss 2, p 59 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/2/59/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11020059","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 11; Issue 2; Pages: 59","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11020059","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11020059","pdf_url":"https://www.mdpi.com/2075-1680/11/2/59/pdf?version=1644549583","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4210581943.pdf","grobid_xml":"https://content.openalex.org/works/W4210581943.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W106832483","https://openalex.org/W1935132094","https://openalex.org/W1973831029","https://openalex.org/W2034292086","https://openalex.org/W2134347681","https://openalex.org/W2140673263","https://openalex.org/W2307374346","https://openalex.org/W2570949444","https://openalex.org/W2900592462","https://openalex.org/W2913624002","https://openalex.org/W2978322662","https://openalex.org/W2991624536","https://openalex.org/W2991625627","https://openalex.org/W3012246947","https://openalex.org/W3200960688","https://openalex.org/W4301101863","https://openalex.org/W6604364948","https://openalex.org/W6612963295","https://openalex.org/W6640459190","https://openalex.org/W6679956567","https://openalex.org/W6771002009","https://openalex.org/W6771678196"],"related_works":["https://openalex.org/W3038906685","https://openalex.org/W2392975301","https://openalex.org/W2259363500","https://openalex.org/W2387543012","https://openalex.org/W4297809691","https://openalex.org/W2620974800","https://openalex.org/W4287077343","https://openalex.org/W2368479431","https://openalex.org/W3182949439","https://openalex.org/W2084445308"],"abstract_inverted_index":{"We":[0,51],"introduce":[1],"the":[2,48,61],"notion":[3],"of":[4,15,63],"a":[5,64],"Pythagorean":[6],"hypersurface":[7,33],"immersed":[8],"into":[9],"an":[10,31],"n+1-dimensional":[11],"pseudo-Riemannian":[12],"space":[13],"form":[14],"constant":[16],"sectional":[17,42],"curvature":[18,43],"c\u2208\u22121,0,1.":[19],"By":[20],"using":[21],"this":[22,54],"definition,":[23],"we":[24],"prove":[25],"in":[26],"Riemannian":[27],"setting":[28],"that":[29],"if":[30],"isoparametric":[32],"is":[34,38,47],"Pythagorean,":[35],"then":[36],"it":[37],"totally":[39,66],"umbilical":[40,67],"with":[41],"\u03c6+c,":[44],"where":[45],"\u03c6":[46],"Golden":[49],"Ratio.":[50],"also":[52],"extend":[53],"result":[55],"to":[56],"Lorentzian":[57],"ambient":[58],"space,":[59],"observing":[60],"existence":[62],"non":[65],"model.":[68]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-02-08T00:00:00"}