{"id":"https://openalex.org/W7221095337","doi":"https://doi.org/10.48550/arxiv.2610.11209","title":"On Ricci solitons whose level hypersurfaces have parallel second fundamental form","display_name":"On Ricci solitons whose level hypersurfaces have parallel second fundamental form","publication_year":2026,"publication_date":"2026-10-08","ids":{"openalex":"https://openalex.org/W7221095337","doi":"https://doi.org/10.48550/arxiv.2610.11209"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.11209","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.11209","pdf_url":"https://arxiv.org/pdf/2610.11209","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/2610.11209","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120026667","display_name":"Matheus Andrade Ribeiro de Moura Hor\u00e1cio","orcid":"https://orcid.org/0009-0001-5658-7467","observed_orcids":["https://orcid.org/0009-0001-5658-7467"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hor\u00e1cio, Matheus Andrade Ribeiro de Moura","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5120026667"],"corresponding_institution_ids":[],"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9955999851226807,"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":0.9955999851226807,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.0038999998942017555,"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":0.0005000000237487257,"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":0.9599999785423279},{"id":"https://openalex.org/keywords/parallel-second-fundamental-form","display_name":"parallel second fundamental form","score":0.996999979019165},{"id":"https://openalex.org/keywords/constant-scalar-curvature","display_name":"constant scalar curvature","score":0.7919999957084656},{"id":"https://openalex.org/keywords/rigidity","display_name":"rigidity","score":0.7960000038146973},{"id":"https://openalex.org/keywords/gradient-shrinking-ricci-solitons","display_name":"gradient shrinking Ricci solitons","score":0.8899999856948853},{"id":"https://openalex.org/keywords/principal-curvatures","display_name":"principal curvatures","score":0.718999981880188}],"concepts":[{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.8528000116348267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7662000060081482},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.6517999768257141},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.58160001039505},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5575000047683716},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.5271000266075134},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5072000026702881},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4771000146865845},{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.44920000433921814},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.42800000309944153},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4230000078678131},{"id":"https://openalex.org/C148729565","wikidata":"https://www.wikidata.org/wiki/Q1361396","display_name":"Ricci flow","level":4,"score":0.4163999855518341},{"id":"https://openalex.org/C119830904","wikidata":"https://www.wikidata.org/wiki/Q233220","display_name":"Second fundamental form","level":4,"score":0.3984000086784363},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3698999881744385},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C16977076","wikidata":"https://www.wikidata.org/wiki/Q1589551","display_name":"Principal curvature","level":4,"score":0.28439998626708984},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C146674193","wikidata":"https://www.wikidata.org/wiki/Q40139","display_name":"Curvature of Riemannian manifolds","level":5,"score":0.26330000162124634}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.11209","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.11209","pdf_url":"https://arxiv.org/pdf/2610.11209","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.2610.11209","doi":"https://doi.org/10.48550/arxiv.2610.11209","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.11209","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:2610.11209","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.11209","pdf_url":"https://arxiv.org/pdf/2610.11209","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":[{"id":"https://openalex.org/F4320310929","display_name":"Universidade de Bras\u00edlia","ror":"https://ror.org/02xfp8v59"},{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221095337.pdf","grobid_xml":"https://content.openalex.org/works/W7221095337.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3126668166","https://openalex.org/W2057813131","https://openalex.org/W7214382778","https://openalex.org/W2085872984","https://openalex.org/W2725870026","https://openalex.org/W2953206944","https://openalex.org/W7114932400","https://openalex.org/W7214899519","https://openalex.org/W3210064892","https://openalex.org/W2964047378"],"abstract_inverted_index":{"We":[0,16,61,134],"study":[1],"gradient":[2,72,100,127,140],"Ricci":[3,59,73,89,101,129,142],"solitons":[4,130],"whose":[5,144],"potential":[6,36],"functions":[7],"have":[8,148],"level":[9,79,114,146],"hypersurfaces":[10,147],"with":[11,35,103,131],"parallel":[12,82,87,149],"second":[13,83,150],"fundamental":[14,84,151],"form.":[15],"show":[17],"that":[18,52,64,96,137],"such":[19],"a":[20,24,29,97,138],"soliton":[21,74,102,143],"is":[22,107,160],"locally":[23],"multiply":[25,49],"warped":[26,50],"product":[27],"of":[28,58,123],"one-dimensional":[30],"base":[31],"and":[32,86,153],"Einstein":[33],"fibers,":[34],"function":[37],"depending":[38],"only":[39],"on":[40,165],"the":[41,48,65,121,166],"base.":[42],"Thus,":[43],"locally,":[44],"this":[45,117,132],"condition":[46],"characterizes":[47],"structure":[51,68],"occurs":[53],"in":[54],"many":[55],"classical":[56],"constructions":[57],"solitons.":[60],"further":[62],"prove":[63,95,136],"same":[66],"local":[67],"follows":[69],"for":[70,126],"any":[71,163],"if":[75],"just":[76],"one":[77,112,156],"regular":[78,113,145],"hypersurface":[80,115],"has":[81,116],"form":[85,152],"intrinsic":[88],"tensor.":[90],"As":[91],"an":[92],"application,":[93],"we":[94],"complete":[98,139],"nonsteady":[99],"constant":[104],"scalar":[105,167],"curvature":[106,159],"rigid":[108],"as":[109,111],"soon":[110],"property.":[118,133],"In":[119],"particular,":[120],"conjecture":[122],"Cao":[124],"holds":[125],"shrinking":[128,141],"also":[135],"at":[154],"most":[155],"nonzero":[157],"principal":[158],"rigid,":[161],"without":[162],"assumption":[164],"curvature.":[168]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-10T00:00:00"}