{"id":"https://openalex.org/W7222010418","doi":"https://doi.org/10.48550/arxiv.2610.20568","title":"Complex generalized spin-c Killing spinors in low dimensions","display_name":"Complex generalized spin-c Killing spinors in low dimensions","publication_year":2026,"publication_date":"2026-10-14","ids":{"openalex":"https://openalex.org/W7222010418","doi":"https://doi.org/10.48550/arxiv.2610.20568"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.20568","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.20568","pdf_url":"https://arxiv.org/pdf/2610.20568","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/2610.20568","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158796560","display_name":"Jos\u00e9 Luis Carmona Jim\u00e9nez","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jim\u00e9nez, Jos\u00e9 Luis Carmona","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006661159","display_name":"Alejandro Gil-Garc\u00eda","orcid":"https://orcid.org/0000-0002-9370-241X","observed_orcids":["https://orcid.org/0000-0002-9370-241X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gil-Garc\u00eda, Alejandro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5158824711","display_name":"C. S. Shahbazi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shahbazi, C. S.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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":0.8485999703407288,"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":0.8485999703407288,"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":0.11940000206232071,"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":0.017999999225139618,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/riemannian-surfaces","display_name":"Riemannian surfaces","score":0.9259999990463257},{"id":"https://openalex.org/keywords/trans-sasakian-manifolds","display_name":"trans-Sasakian manifolds","score":0.8840000033378601},{"id":"https://openalex.org/keywords/3-manifolds","display_name":"3-manifolds","score":0.6809999942779541},{"id":"https://openalex.org/keywords/characteristic-vector-field","display_name":"characteristic vector field","score":0.7310000061988831}],"concepts":[{"id":"https://openalex.org/C43506125","wikidata":"https://www.wikidata.org/wiki/Q604907","display_name":"Spinor","level":2,"score":0.8263000249862671},{"id":"https://openalex.org/C42519931","wikidata":"https://www.wikidata.org/wiki/Q1200279","display_name":"Killing vector field","level":2,"score":0.7745000123977661},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6380000114440918},{"id":"https://openalex.org/C2779761358","wikidata":"https://www.wikidata.org/wiki/Q6407805","display_name":"Killing spinor","level":4,"score":0.6244000196456909},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.546500027179718},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.47999998927116394},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4690000116825104},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43810001015663147},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.39750000834465027},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3849000036716461},{"id":"https://openalex.org/C200347057","wikidata":"https://www.wikidata.org/wiki/Q3254711","display_name":"Spinor field","level":3,"score":0.3813999891281128},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.366100013256073},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.32820001244544983},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C193718343","wikidata":"https://www.wikidata.org/wiki/Q7261160","display_name":"Pure spinor","level":4,"score":0.2565999925136566},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2563000023365021}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.20568","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.20568","pdf_url":"https://arxiv.org/pdf/2610.20568","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.2610.20568","doi":"https://doi.org/10.48550/arxiv.2610.20568","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.20568","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:2610.20568","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.20568","pdf_url":"https://arxiv.org/pdf/2610.20568","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/W7222010418.pdf","grobid_xml":"https://content.openalex.org/works/W7222010418.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W206680636","https://openalex.org/W2006464342","https://openalex.org/W2009804972","https://openalex.org/W2010100728","https://openalex.org/W2063184439","https://openalex.org/W2085893669","https://openalex.org/W2125144362","https://openalex.org/W2151931670","https://openalex.org/W4312934976","https://openalex.org/W4417070141","https://openalex.org/W7160825507","https://openalex.org/W7162114384","https://openalex.org/W7164153385","https://openalex.org/W7203877197"],"related_works":["https://openalex.org/W2125144362","https://openalex.org/W7164153385","https://openalex.org/W7160825507","https://openalex.org/W1967251742","https://openalex.org/W7162013148","https://openalex.org/W7143803730","https://openalex.org/W7095870841","https://openalex.org/W2082389893","https://openalex.org/W4407241277","https://openalex.org/W7166832381"],"abstract_inverted_index":{"We":[0,25,48,69],"classify":[1],"all":[2,22],"complex":[3,9,37,83,89,118,173,178],"generalized":[4,38,84,119,179],"spin-c":[5,39,78,85,120,180],"Killing":[6,10,40,86,90,121,174,181],"spinors":[7,41],"with":[8,88,116],"function":[11,91,175],"$i\u03bc-\u03b1$":[12,92],"on":[13,42,166],"complete":[14,59,63],"Riemannian":[15,43,79,113,170],"surfaces,":[16],"presenting":[17],"an":[18],"explicit":[19,55],"list":[20],"of":[21,103,144,176],"possible":[23,138],"cases.":[24],"show":[26],"that,":[27],"contrary":[28],"to":[29,72],"previous":[30],"statements":[31],"in":[32,161],"the":[33,50,140,145,172],"literature,":[34],"there":[35],"exist":[36],"surfaces":[44],"for":[45,65,123],"which":[46,66,124],"$\u03b1\u03bc\\not\\equiv0$.":[47],"illustrate":[49],"classification":[51],"by":[52,156],"providing":[53],"several":[54],"local,":[56],"compact,":[57],"and":[58,94,131,158,168],"examples,":[60],"including":[61],"a":[62,77,82,99,110,117,154],"example":[64],"$\u03b1\u03bc>0$":[67],"everywhere.":[68],"then":[70,132],"move":[71],"three":[73],"dimensions,":[74],"proving":[75],"that":[76,134,165],"three-manifold":[80,114],"admits":[81],"spinor":[87,122,182],"if":[93,96,139],"only":[95],"it":[97],"is":[98,136,149],"$\u03bc$-exact":[100],"trans-Sasakian":[101,147],"manifold":[102],"type":[104],"$(\u03b1,\u03bc)$.":[105],"In":[106],"addition,":[107],"we":[108],"construct":[109],"geodesically":[111],"incomplete":[112],"equipped":[115],"neither":[125],"$\u03bc$":[126],"nor":[127],"$\u03b1$":[128],"vanishes":[129],"identically,":[130],"prove":[133],"this":[135],"not":[137],"characteristic":[141],"vector":[142],"field":[143],"associated":[146],"structure":[148],"complete.":[150],"These":[151],"results":[152],"settle":[153],"conjecture":[155],"Gro\u00dfe":[157],"Nakad":[159],"(Results":[160],"Mathematics,":[162],"2015)":[163],"stating":[164],"two-":[167],"three-dimensional":[169],"manifolds":[171],"any":[177],"must":[183],"be":[184],"either":[185],"globally":[186,189],"real":[187],"or":[188],"imaginary.":[190]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-16T00:00:00"}