{"id":"https://openalex.org/W7214972835","doi":"https://doi.org/10.48550/arxiv.2609.36095","title":"A Note on the Classification of Centroaffine Hypersurfaces","display_name":"A Note on the Classification of Centroaffine Hypersurfaces","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214972835","doi":"https://doi.org/10.48550/arxiv.2609.36095"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.36095","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36095","pdf_url":"https://arxiv.org/pdf/2609.36095","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.36095","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026109715","display_name":"Zuzanna Szancer","orcid":"https://orcid.org/0000-0003-3538-9557","observed_orcids":["https://orcid.org/0000-0003-3538-9557"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Szancer, Zuzanna","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5026109715"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9965999722480774,"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":0.9965999722480774,"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":0.0015999999595806003,"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":9.999999747378752e-05,"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/classification-of-hypersurfaces","display_name":"classification of hypersurfaces","score":0.8360000252723694},{"id":"https://openalex.org/keywords/affine-differential-geometry","display_name":"affine differential geometry","score":0.4690000116825104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7669000029563904},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5411999821662903},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5379999876022339},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.508400022983551},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.453000009059906},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.4489000141620636},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.44519999623298645},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4260999858379364},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.38440001010894775},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.33719998598098755},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2953999936580658},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.2897999882698059},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.2766999900341034},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2736000120639801},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2612999975681305},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.25429999828338623}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.36095","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36095","pdf_url":"https://arxiv.org/pdf/2609.36095","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.36095","doi":"https://doi.org/10.48550/arxiv.2609.36095","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.36095","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.36095","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36095","pdf_url":"https://arxiv.org/pdf/2609.36095","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214972835.pdf","grobid_xml":"https://content.openalex.org/works/W7214972835.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2579620926","https://openalex.org/W2012639418","https://openalex.org/W2592877081","https://openalex.org/W2040767563","https://openalex.org/W4285390475","https://openalex.org/W7203644409","https://openalex.org/W2945040897","https://openalex.org/W7160717475","https://openalex.org/W2335396917","https://openalex.org/W2550199760"],"abstract_inverted_index":{"Cao":[0],"and":[1,21,59],"Wang":[2],"recently":[3],"classified":[4],"a":[5],"class":[6],"of":[7,44],"locally":[8],"strongly":[9],"convex":[10],"centroaffine":[11],"hypersurfaces":[12],"whose":[13],"non-vanishing":[14],"Tchebychev":[15],"vector":[16],"field":[17],"$T$":[18],"satisfies":[19],"$K(T,X)=\u03b1X$":[20],"$X(\u03b1)=0$":[22],"for":[23],"every":[24],"$X\\perp":[25],"T$,":[26],"together":[27],"with":[28],"$K(T,T)=\u03b2T$.":[29],"In":[30],"the":[31,42,45,60],"degenerate":[32],"case":[33],"$\u03b2=2\u03b1$,":[34],"their":[35],"higher-dimensional":[36],"argument":[37],"assumes":[38],"in":[39],"addition":[40],"that":[41,53],"$T^\\perp$-component":[43],"difference":[46],"tensor":[47],"$K$":[48],"vanishes":[49],"identically.":[50],"We":[51],"show":[52],"this":[54],"extra":[55],"assumption":[56],"is":[57],"unnecessary":[58],"theorem":[61],"can":[62],"be":[63],"strengthened.":[64]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-01T00:00:00"}