{"id":"https://openalex.org/W7213605116","doi":"https://doi.org/10.48550/arxiv.2609.19568","title":"Infinitesimmaly homogeneous manifolds with symplectic and almost contact structure groups","display_name":"Infinitesimmaly homogeneous manifolds with symplectic and almost contact structure groups","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213605116","doi":"https://doi.org/10.48550/arxiv.2609.19568"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.19568","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19568","pdf_url":"https://arxiv.org/pdf/2609.19568","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/2609.19568","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153514977","display_name":"Carlos Alberto Mar\u00edn Arango","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arango, Carlos Alberto Mar\u00edn","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5149155091","display_name":"Alejandro Pinilla Barrera","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I35961687","display_name":"Universidad de Antioquia","ror":"https://ror.org/03bp5hc83","country_code":"CO","type":"education","lineage":["https://openalex.org/I35961687"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"Barrera, Alejandro Pinilla","raw_affiliation_strings":["INSTITUTO DE MATEM \u00c1TICAS Y ESTAD\u00cdSTICA , FACULTAD DE CIENCIAS EXACTAS Y NATURALES , UNIVERSIDAD DE ANTIOQUIA , MEDELL\u00cdN , COLOMBIA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INSTITUTO DE MATEM \u00c1TICAS Y ESTAD\u00cdSTICA , FACULTAD DE CIENCIAS EXACTAS Y NATURALES , UNIVERSIDAD DE ANTIOQUIA , MEDELL\u00cdN , COLOMBIA","institution_ids":["https://openalex.org/I35961687"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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":0.9994999766349792,"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":0.9994999766349792,"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":0.00019999999494757503,"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/T10304","display_name":"Geometric and Algebraic Topology","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/affine-manifolds","display_name":"affine manifolds","score":0.8399999737739563},{"id":"https://openalex.org/keywords/almost-contact-metric-structures","display_name":"almost contact metric structures","score":0.871999979019165},{"id":"https://openalex.org/keywords/structure-group","display_name":"structure group","score":0.6970000267028809}],"concepts":[{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.8644000291824341},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7689999938011169},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.745199978351593},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.6603000164031982},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6126000285148621},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.597000002861023},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.5210000276565552},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5200999975204468},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.5181000232696533},{"id":"https://openalex.org/C105561566","wikidata":"https://www.wikidata.org/wiki/Q1371213","display_name":"Affine connection","level":3,"score":0.45089998841285706},{"id":"https://openalex.org/C62623296","wikidata":"https://www.wikidata.org/wiki/Q686291","display_name":"Affine group","level":3,"score":0.44929999113082886},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.40689998865127563},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3862000107765198},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.3637999892234802},{"id":"https://openalex.org/C153011950","wikidata":"https://www.wikidata.org/wiki/Q10310534","display_name":"Infinitesimal transformation","level":3,"score":0.3434000015258789},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C40265840","wikidata":"https://www.wikidata.org/wiki/Q6897118","display_name":"Moment map","level":3,"score":0.322299987077713},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C135661100","wikidata":"https://www.wikidata.org/wiki/Q1049064","display_name":"Symplectomorphism","level":3,"score":0.3109999895095825},{"id":"https://openalex.org/C23684344","wikidata":"https://www.wikidata.org/wiki/Q382520","display_name":"Affine geometry","level":4,"score":0.29809999465942383},{"id":"https://openalex.org/C202411454","wikidata":"https://www.wikidata.org/wiki/Q4688941","display_name":"Affine geometry of curves","level":4,"score":0.2913999855518341},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.2621000111103058},{"id":"https://openalex.org/C104586451","wikidata":"https://www.wikidata.org/wiki/Q771008","display_name":"Symplectic representation","level":4,"score":0.2612999975681305},{"id":"https://openalex.org/C95565831","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine coordinate system","level":4,"score":0.26080000400543213},{"id":"https://openalex.org/C205633959","wikidata":"https://www.wikidata.org/wiki/Q2494915","display_name":"Unipotent","level":2,"score":0.2554999887943268},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.2531999945640564},{"id":"https://openalex.org/C74544821","wikidata":"https://www.wikidata.org/wiki/Q1783105","display_name":"Contact geometry","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.19568","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19568","pdf_url":"https://arxiv.org/pdf/2609.19568","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.2609.19568","doi":"https://doi.org/10.48550/arxiv.2609.19568","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.19568","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:2609.19568","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.19568","pdf_url":"https://arxiv.org/pdf/2609.19568","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/W7213605116.pdf","grobid_xml":"https://content.openalex.org/works/W7213605116.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2949145422"],"related_works":["https://openalex.org/W2255940924","https://openalex.org/W2047869641","https://openalex.org/W7095081120","https://openalex.org/W2183620241","https://openalex.org/W2047553800","https://openalex.org/W7099748482","https://openalex.org/W1488820363","https://openalex.org/W2043518438","https://openalex.org/W2344109516","https://openalex.org/W2925907635"],"abstract_inverted_index":{"We":[0,90],"study":[1],"infinitesimally":[2,23],"homogeneous":[3,24],"affine":[4,31],"manifolds":[5],"with":[6],"prescribed":[7],"structure":[8],"groups.":[9],"First,":[10],"for":[11,34],"the":[12,21,47,53,74,93,98],"real":[13],"symplectic":[14,30],"group":[15],"$\\operatorname{Sp}(2n,\\mathbb":[16],"R)$,":[17],"we":[18,45],"prove":[19],"that":[20],"corresponding":[22],"structures":[25],"are":[26,38,66],"precisely":[27,79],"flat":[28],"torsion-free":[29,48,99],"structures.":[32],"Second,":[33],"\\(\\operatorname{U}(n)\\times\\{1\\}\\),":[35],"whose":[36],"\\(G\\)-structures":[37],"equivalent":[39],"to":[40,101],"almost":[41],"contact":[42,78],"metric":[43],"data,":[44],"classify":[46],"characteristic":[49],"tensors":[50],"and":[51,63,73,96],"obtain":[52],"general":[54],"torsional":[55],"case":[56],"by":[57,68],"invariant":[58],"deformation.":[59],"The":[60],"admissible":[61],"torsion":[62],"inner-torsion":[64],"parameters":[65,86],"governed":[67],"a":[69,81],"single":[70],"algebraic":[71],"relation,":[72],"horizontal":[75],"distribution":[76],"is":[77],"when":[80],"certain":[82],"combination":[83],"of":[84],"these":[85],"does":[87],"not":[88],"vanish.":[89],"also":[91],"describe":[92],"compatible":[94],"connections":[95],"relate":[97],"branches":[100],"trans-Sasakian":[102],"geometry.":[103]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-19T00:00:00"}