{"id":"https://openalex.org/W4406325760","doi":"https://doi.org/10.3390/axioms14010056","title":"On the Work of Cartan and M\u00fcnzner on Isoparametric Hypersurfaces","display_name":"On the Work of Cartan and M\u00fcnzner on Isoparametric Hypersurfaces","publication_year":2025,"publication_date":"2025-01-13","ids":{"openalex":"https://openalex.org/W4406325760","doi":"https://doi.org/10.3390/axioms14010056"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14010056","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14010056","pdf_url":"https://www.mdpi.com/2075-1680/14/1/56/pdf?version=1736773468","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/2075-1680/14/1/56/pdf?version=1736773468","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042605317","display_name":"Thomas E. Cecil","orcid":"https://orcid.org/0000-0002-0994-9314"},"institutions":[{"id":"https://openalex.org/I107139065","display_name":"College of the Holy Cross","ror":"https://ror.org/05dwp6855","country_code":"US","type":"education","lineage":["https://openalex.org/I107139065"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Thomas E. Cecil","raw_affiliation_strings":["Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01610, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01610, USA","institution_ids":["https://openalex.org/I107139065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046618498","display_name":"Patrick J. Ryan","orcid":"https://orcid.org/0000-0003-2384-7207"},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Patrick J. Ryan","raw_affiliation_strings":["Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S4K1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S4K1, Canada","institution_ids":["https://openalex.org/I98251732"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042605317"],"corresponding_institution_ids":["https://openalex.org/I107139065"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":4.0483,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.86749475,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"14","issue":"1","first_page":"56","last_page":"56"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9929999709129333,"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":0.9929999709129333,"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":0.9735999703407288,"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/T12351","display_name":"Geometry and complex manifolds","score":0.9508000016212463,"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":0.8704475164413452},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5479507446289062},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4745907485485077},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.461184561252594},{"id":"https://openalex.org/keywords/preprint","display_name":"Preprint","score":0.4481911063194275},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4420015811920166},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.42418137192726135},{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.4146007001399994},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.19309669733047485},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16785761713981628},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13416066765785217}],"concepts":[{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.8704475164413452},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5479507446289062},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4745907485485077},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.461184561252594},{"id":"https://openalex.org/C43169469","wikidata":"https://www.wikidata.org/wiki/Q580922","display_name":"Preprint","level":2,"score":0.4481911063194275},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4420015811920166},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.42418137192726135},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.4146007001399994},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.19309669733047485},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16785761713981628},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13416066765785217},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14010056","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14010056","pdf_url":"https://www.mdpi.com/2075-1680/14/1/56/pdf?version=1736773468","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:4b4ae7753134412baf81fd751d8642b3","is_oa":true,"landing_page_url":"https://doaj.org/article/4b4ae7753134412baf81fd751d8642b3","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 1, p 56 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14010056","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14010056","pdf_url":"https://www.mdpi.com/2075-1680/14/1/56/pdf?version=1736773468","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/W4406325760.pdf","grobid_xml":"https://content.openalex.org/works/W4406325760.grobid-xml"},"referenced_works_count":67,"referenced_works":["https://openalex.org/W87494860","https://openalex.org/W157927367","https://openalex.org/W1482911014","https://openalex.org/W1513885689","https://openalex.org/W1535636603","https://openalex.org/W1549864584","https://openalex.org/W1566596520","https://openalex.org/W1568295503","https://openalex.org/W1583911619","https://openalex.org/W1584769248","https://openalex.org/W1585928768","https://openalex.org/W1935132094","https://openalex.org/W1976469870","https://openalex.org/W1977083091","https://openalex.org/W1982170949","https://openalex.org/W2009962042","https://openalex.org/W2018351175","https://openalex.org/W2022055730","https://openalex.org/W2024024636","https://openalex.org/W2035898622","https://openalex.org/W2039108329","https://openalex.org/W2052841982","https://openalex.org/W2057552658","https://openalex.org/W2060878503","https://openalex.org/W2063921502","https://openalex.org/W2076002049","https://openalex.org/W2079773617","https://openalex.org/W2091791701","https://openalex.org/W2104250124","https://openalex.org/W2106024031","https://openalex.org/W2132689828","https://openalex.org/W2132949357","https://openalex.org/W2134347681","https://openalex.org/W2150538504","https://openalex.org/W2239661582","https://openalex.org/W2319136128","https://openalex.org/W2319346282","https://openalex.org/W2321699222","https://openalex.org/W2330712617","https://openalex.org/W2340123041","https://openalex.org/W2340352145","https://openalex.org/W2727703779","https://openalex.org/W2891478334","https://openalex.org/W2904413215","https://openalex.org/W2914550877","https://openalex.org/W2914887028","https://openalex.org/W2963417027","https://openalex.org/W2963447914","https://openalex.org/W2963743038","https://openalex.org/W2963859328","https://openalex.org/W2986242450","https://openalex.org/W4210801347","https://openalex.org/W4213429738","https://openalex.org/W4231380312","https://openalex.org/W4233041924","https://openalex.org/W4234279903","https://openalex.org/W4234970518","https://openalex.org/W4237652863","https://openalex.org/W4242109993","https://openalex.org/W4250537889","https://openalex.org/W6637285476","https://openalex.org/W6640459190","https://openalex.org/W6679956567","https://openalex.org/W6754587936","https://openalex.org/W6757338390","https://openalex.org/W6779992095","https://openalex.org/W7029382108"],"related_works":["https://openalex.org/W4229365511","https://openalex.org/W3131332557","https://openalex.org/W4211247774","https://openalex.org/W3045462960","https://openalex.org/W4393774512","https://openalex.org/W4393658307","https://openalex.org/W4286761081","https://openalex.org/W4393731985","https://openalex.org/W4210578026","https://openalex.org/W4389362563"],"abstract_inverted_index":{"A":[0],"hypersurface":[1],"Mn":[2],"in":[3,39,43,50,68,71,79,125],"a":[4,23,114],"real":[5,40],"space":[6,41],"form":[7,70],"Rn+1,":[8],"Sn+1,":[9],"or":[10],"Hn+1":[11],"is":[12,22,48],"isoparametric":[13,37,96,123],"if":[14],"it":[15],"has":[16],"constant":[17],"principal":[18],"curvatures.":[19],"This":[20,46],"paper":[21,111],"survey":[24,116],"of":[25,29,36,53,63,83,91,95,117,122],"the":[26,34,57,72,89,92,118],"fundamental":[27],"work":[28,47],"Cartan":[30,54,84],"and":[31,60,75,85,98],"M\u00fcnzner":[32,64,86],"on":[33],"theory":[35],"hypersurfaces":[38,124],"forms,":[42],"particular,":[44],"spheres.":[45,126],"contained":[49],"four":[51],"papers":[52,62,82],"published":[55,67],"during":[56],"period":[58],"1938\u20131940":[59],"two":[61],"that":[65],"were":[66],"preprint":[69],"early":[73],"1970s":[74],"as":[76],"journal":[77],"articles":[78],"1980\u20131981.":[80],"These":[81],"have":[87,100],"been":[88,102],"foundation":[90],"extensive":[93],"field":[94],"hypersurfaces,":[97],"they":[99],"all":[101],"recently":[103,119],"translated":[104],"into":[105],"English":[106],"by":[107],"T.":[108],"Cecil.":[109],"The":[110],"concludes":[112],"with":[113],"brief":[115],"completed":[120],"classification":[121]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-01-14T00:00:00"}
