{"id":"https://openalex.org/W4406612729","doi":"https://doi.org/10.3390/axioms14010068","title":"Sphere Theorems for \u03c3k-Einstein Manifolds","display_name":"Sphere Theorems for \u03c3k-Einstein Manifolds","publication_year":2025,"publication_date":"2025-01-17","ids":{"openalex":"https://openalex.org/W4406612729","doi":"https://doi.org/10.3390/axioms14010068"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14010068","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14010068","pdf_url":"https://www.mdpi.com/2075-1680/14/1/68/pdf?version=1737122261","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/2075-1680/14/1/68/pdf?version=1737122261","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025439589","display_name":"Jingyang Zhong","orcid":"https://orcid.org/0009-0007-1298-9433"},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jingyang Zhong","raw_affiliation_strings":["School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, China"],"raw_orcid":"https://orcid.org/0009-0007-1298-9433","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, China","institution_ids":["https://openalex.org/I80947539"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5115947480","display_name":"Xinran Mu","orcid":null},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinran Mu","raw_affiliation_strings":["School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, China","institution_ids":["https://openalex.org/I80947539"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025439589"],"corresponding_institution_ids":["https://openalex.org/I80947539"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01562935,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"1","first_page":"68","last_page":"68"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9991000294685364,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/einstein","display_name":"Einstein","score":0.7360590696334839},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4671345055103302},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41842442750930786},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3547331690788269},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3533981442451477},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.3488457202911377}],"concepts":[{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.7360590696334839},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4671345055103302},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41842442750930786},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3547331690788269},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3533981442451477},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3488457202911377}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms14010068","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14010068","pdf_url":"https://www.mdpi.com/2075-1680/14/1/68/pdf?version=1737122261","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:03e6cb217efa4a17a84cbfd481697a37","is_oa":true,"landing_page_url":"https://doaj.org/article/03e6cb217efa4a17a84cbfd481697a37","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,"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":"Axioms, Vol 14, Iss 1, p 68 (2025)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/14/1/68/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms14010068","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":"Pages: 68","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms14010068","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14010068","pdf_url":"https://www.mdpi.com/2075-1680/14/1/68/pdf?version=1737122261","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":[{"id":"https://openalex.org/G2384262362","display_name":null,"funder_award_id":"11901100","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406612729.pdf","grobid_xml":"https://content.openalex.org/works/W4406612729.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1131953619","https://openalex.org/W1996946209","https://openalex.org/W2070680292","https://openalex.org/W2964317139","https://openalex.org/W4237656740","https://openalex.org/W4242522601","https://openalex.org/W6649777039"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"A":[0,20],"problem":[1],"that":[2,24,57],"geometers":[3],"have":[4],"always":[5,33],"been":[6],"concerned":[7],"with":[8],"is":[9,14,32,73],"when":[10],"a":[11,17,25,36,39,58,67,76,79],"closed":[12,26,59],"manifold":[13,31,61],"isometric":[15,34,74],"to":[16,35,75],"round":[18,40,80],"sphere.":[19,41,81],"classical":[21],"result":[22],"shows":[23],"locally":[27],"conformally":[28],"flat":[29],"Einstein":[30,71],"quotient":[37,77],"of":[38,49,66,78],"In":[42],"this":[43],"note,":[44],"we":[45,55],"provide":[46],"the":[47],"definitions":[48],"\u03c3k-curvatures":[50],"and":[51,54,70],"\u03c3k-Einstein":[52,60],"manifolds,":[53],"show":[56],"under":[62],"certain":[63],"pinching":[64],"conditions":[65],"Weyl":[68],"curvature":[69,72]},"counts_by_year":[],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}