{"id":"https://openalex.org/W7214899519","doi":"https://doi.org/10.48550/arxiv.2609.36418","title":"K\u00e4hler--Ricci Shrinkers with Constant Scalar Curvature Are Rigid","display_name":"K\u00e4hler--Ricci Shrinkers with Constant Scalar Curvature Are Rigid","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214899519","doi":"https://doi.org/10.48550/arxiv.2609.36418"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.36418","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36418","pdf_url":"https://arxiv.org/pdf/2609.36418","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/2609.36418","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153553054","display_name":"Wenqi Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I161127581","display_name":"Universidade Federal Fluminense","ror":"https://ror.org/02rjhbb08","country_code":"BR","type":"education","lineage":["https://openalex.org/I161127581"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Li, Wenqi","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Estat\u00edstica , Universidade Federal Fluminense , S\u00e3o Domingos , Niter\u00f3i , RJ 24210-201 , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica , Universidade Federal Fluminense , S\u00e3o Domingos , Niter\u00f3i , RJ 24210-201 , Brazil","institution_ids":["https://openalex.org/I161127581"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153591591","display_name":"Jianyu Ou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I161127581","display_name":"Universidade Federal Fluminense","ror":"https://ror.org/02rjhbb08","country_code":"BR","type":"education","lineage":["https://openalex.org/I161127581"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Ou, Jianyu","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Estat\u00edstica , Universidade Federal Fluminense , S\u00e3o Domingos , Niter\u00f3i , RJ 24210-201 , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica , Universidade Federal Fluminense , S\u00e3o Domingos , Niter\u00f3i , RJ 24210-201 , Brazil","institution_ids":["https://openalex.org/I161127581"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083508942","display_name":"Guoqiang Wu","orcid":"https://orcid.org/0000-0001-5689-1808","observed_orcids":["https://orcid.org/0000-0001-5689-1808"]},"institutions":[{"id":"https://openalex.org/I161127581","display_name":"Universidade Federal Fluminense","ror":"https://ror.org/02rjhbb08","country_code":"BR","type":"education","lineage":["https://openalex.org/I161127581"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Wu, Guoqiang","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Estat\u00edstica , Universidade Federal Fluminense , S\u00e3o Domingos , Niter\u00f3i , RJ 24210-201 , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica , Universidade Federal Fluminense , S\u00e3o Domingos , Niter\u00f3i , RJ 24210-201 , Brazil","institution_ids":["https://openalex.org/I161127581"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051076908","display_name":"\u5468\u5fb7\u5802","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I161127581","display_name":"Universidade Federal Fluminense","ror":"https://ror.org/02rjhbb08","country_code":"BR","type":"education","lineage":["https://openalex.org/I161127581"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Zhou, Detang","raw_affiliation_strings":["Instituto de Matem\u00e1tica e Estat\u00edstica , Universidade Federal Fluminense , S\u00e3o Domingos , Niter\u00f3i , RJ 24210-201 , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica , Universidade Federal Fluminense , S\u00e3o Domingos , Niter\u00f3i , RJ 24210-201 , Brazil","institution_ids":["https://openalex.org/I161127581"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I161127581"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T12351","display_name":"Geometry and complex manifolds","score":0.9696999788284302,"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/T12351","display_name":"Geometry and complex manifolds","score":0.9696999788284302,"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":0.02979999966919422,"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/T10061","display_name":"Algebraic Geometry and Number Theory","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/gradient-ricci-solitons","display_name":"gradient Ricci solitons","score":0.9039999842643738},{"id":"https://openalex.org/keywords/constant-scalar-curvature","display_name":"constant scalar curvature","score":0.9800000190734863},{"id":"https://openalex.org/keywords/rigidity","display_name":"rigidity","score":0.9200000166893005},{"id":"https://openalex.org/keywords/kahler-einstein-metrics","display_name":"K\u00e4hler-Einstein metrics","score":0.8830000162124634},{"id":"https://openalex.org/keywords/product-spaces","display_name":"product spaces","score":0.33500000834465027}],"concepts":[{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.7232000231742859},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7107999920845032},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5859000086784363},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.5673999786376953},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5159000158309937},{"id":"https://openalex.org/C2778530986","wikidata":"https://www.wikidata.org/wiki/Q5457948","display_name":"Flatness (cosmology)","level":3,"score":0.4966999888420105},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.48179998993873596},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.43860000371932983},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.43389999866485596},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.39480000734329224},{"id":"https://openalex.org/C2779668893","wikidata":"https://www.wikidata.org/wiki/Q2250422","display_name":"Constant curvature","level":3,"score":0.3630000054836273},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.3449999988079071},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.34290000796318054},{"id":"https://openalex.org/C14196021","wikidata":"https://www.wikidata.org/wiki/Q7240881","display_name":"Prescribed scalar curvature problem","level":5,"score":0.3395000100135803},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.3343000113964081},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.289900004863739},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C31836371","wikidata":"https://www.wikidata.org/wiki/Q1856609","display_name":"Scalar potential","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25850000977516174},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.25600001215934753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.36418","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36418","pdf_url":"https://arxiv.org/pdf/2609.36418","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.2609.36418","doi":"https://doi.org/10.48550/arxiv.2609.36418","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.36418","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.36418","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36418","pdf_url":"https://arxiv.org/pdf/2609.36418","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214899519.pdf","grobid_xml":"https://content.openalex.org/works/W7214899519.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W4403569970","https://openalex.org/W4404570074","https://openalex.org/W4414893842","https://openalex.org/W6947953298","https://openalex.org/W7203933971","https://openalex.org/W7214382778"],"related_works":["https://openalex.org/W7221142762","https://openalex.org/W7214382778","https://openalex.org/W7203933971","https://openalex.org/W4200608473","https://openalex.org/W4311411127","https://openalex.org/W7157150767","https://openalex.org/W3175412255","https://openalex.org/W4413378272","https://openalex.org/W1993544335","https://openalex.org/W1991464804"],"abstract_inverted_index":{"Let":[0],"$(M^{2m},g,f,J)$":[1],"be":[2],"a":[3,65,70],"complete":[4,71],"gradient":[5,73],"K\u00e4hler--Ricci":[6],"shrinker":[7],"satisfying":[8],"\\[":[9,37,42,54],"\\operatorname{Ric}+\\nabla^2":[10],"f=\\frac12":[11],"g.":[12],"\\]":[13,40,48,57],"We":[14],"prove":[15],"that":[16,36],"if":[17],"the":[18,24,61,80],"scalar":[19,78],"curvature":[20],"is":[21,26,51],"constant,":[22],"then":[23],"soliton":[25,75],"rigid.":[27],"More":[28],"precisely,":[29],"there":[30],"exists":[31],"an":[32],"integer":[33],"$k\\in\\{0,\\ldots,m\\}$":[34],"such":[35],"R\\equiv":[38],"k":[39],"and":[41,53,87],"(M^{2m},g,J)\\cong":[43],"\\bigl(N^{2k}\\times\\mathbb":[44],"C^{m-k},":[45],"g_N+g_{\\mathrm{Euc}},J_N\\oplus":[46],"J_0\\bigr),":[47],"where":[49],"$(N^{2k},g_N,J_N)$":[50],"K\u00e4hler--Einstein":[52],"\\operatorname{Ric}_{g_N}=\\frac12":[55],"g_N.":[56],"As":[58],"part":[59],"of":[60],"proof,":[62],"we":[63],"establish":[64],"Riemannian":[66],"rigidity":[67],"criterion:":[68],"for":[69],"nonsteady":[72],"Ricci":[74],"with":[76],"constant":[77],"curvature,":[79],"condition":[81],"$\\mathcal{L}_{\\nabla":[82],"f}\\operatorname{Ric}=0$":[83],"implies":[84],"radial":[85],"flatness":[86],"hence":[88],"rigidity.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}