{"id":"https://openalex.org/W7168300545","doi":"https://doi.org/10.48550/arxiv.2607.11804","title":"Bi-Lagrangian and transverse Dirac structures induced on the Whitney sum","display_name":"Bi-Lagrangian and transverse Dirac structures induced on the Whitney sum","publication_year":2026,"publication_date":"2026-07-13","ids":{"openalex":"https://openalex.org/W7168300545","doi":"https://doi.org/10.48550/arxiv.2607.11804"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2607.11804","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.11804","pdf_url":"https://arxiv.org/pdf/2607.11804","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2607.11804","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057477596","display_name":"Bertuel Tangue Ndawa","orcid":"https://orcid.org/0000-0001-8995-9522","observed_orcids":["https://orcid.org/0000-0001-8995-9522"]},"institutions":[{"id":"https://openalex.org/I59196294","display_name":"University of Ngaound\u00e9r\u00e9","ror":"https://ror.org/03gq1d339","country_code":"CM","type":"education","lineage":["https://openalex.org/I59196294"]}],"countries":["CM"],"is_corresponding":false,"raw_author_name":"Ndawa, Bertuel Tangue","raw_affiliation_strings":["University of Ngaoundere , Cameroon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Ngaoundere , Cameroon","institution_ids":["https://openalex.org/I59196294"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056824942","display_name":"Ferdinand Ngakeu","orcid":"https://orcid.org/0000-0003-0321-5501","observed_orcids":["https://orcid.org/0000-0003-0321-5501"]},"institutions":[{"id":"https://openalex.org/I163423212","display_name":"University of Douala","ror":"https://ror.org/02zr5jr81","country_code":"CM","type":"education","lineage":["https://openalex.org/I163423212"]}],"countries":["CM"],"is_corresponding":false,"raw_author_name":"Ngakeu, Ferdinand","raw_affiliation_strings":["University of Douala , Cameroona "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Douala , Cameroona ","institution_ids":["https://openalex.org/I163423212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5119833539","display_name":"Nasser Saipele Nansidi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I213072177","display_name":"University of Maroua","ror":"https://ror.org/051sa4h84","country_code":"CM","type":"education","lineage":["https://openalex.org/I213072177"]}],"countries":["CM"],"is_corresponding":false,"raw_author_name":"Nansidi, Nasser Saipele","raw_affiliation_strings":["University of Maroua , Cameroon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Maroua , Cameroon","institution_ids":["https://openalex.org/I213072177"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":0.8036999702453613,"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"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.8036999702453613,"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"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.0681999996304512,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.03350000083446503,"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/symplectomorphism-groups","display_name":"symplectomorphism groups","score":0.8949999809265137},{"id":"https://openalex.org/keywords/tangent-bundle","display_name":"tangent bundle","score":0.8700000047683716},{"id":"https://openalex.org/keywords/cotangent-bundle","display_name":"cotangent bundle","score":1.0},{"id":"https://openalex.org/keywords/parallelizable-manifolds","display_name":"parallelizable manifolds","score":0.8960000276565552},{"id":"https://openalex.org/keywords/linear-connections","display_name":"linear connections","score":0.6690000295639038}],"concepts":[{"id":"https://openalex.org/C7979169","wikidata":"https://www.wikidata.org/wiki/Q1142143","display_name":"Cotangent bundle","level":3,"score":0.8525000214576721},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6990000009536743},{"id":"https://openalex.org/C135661100","wikidata":"https://www.wikidata.org/wiki/Q1049064","display_name":"Symplectomorphism","level":3,"score":0.5928999781608582},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.5412999987602234},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5385000109672546},{"id":"https://openalex.org/C131715654","wikidata":"https://www.wikidata.org/wiki/Q288465","display_name":"Group action","level":3,"score":0.5338000059127808},{"id":"https://openalex.org/C28903235","wikidata":"https://www.wikidata.org/wiki/Q746550","display_name":"Tangent bundle","level":3,"score":0.5029000043869019},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4708999991416931},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4311999976634979},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4074000120162964},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.4041000008583069},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.39739999175071716},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.3790000081062317},{"id":"https://openalex.org/C66384103","wikidata":"https://www.wikidata.org/wiki/Q2370925","display_name":"Normal bundle","level":3,"score":0.3736000061035156},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3564999997615814},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.3330000042915344},{"id":"https://openalex.org/C99679407","wikidata":"https://www.wikidata.org/wiki/Q56761637","display_name":"Substructure","level":2,"score":0.28139999508857727}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2607.11804","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.11804","pdf_url":"https://arxiv.org/pdf/2607.11804","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2607.11804","doi":"https://doi.org/10.48550/arxiv.2607.11804","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.11804","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:2607.11804","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.11804","pdf_url":"https://arxiv.org/pdf/2607.11804","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":"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/W7168300545.pdf","grobid_xml":"https://content.openalex.org/works/W7168300545.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2150863671","https://openalex.org/W1984098702","https://openalex.org/W2182320071","https://openalex.org/W4402289869","https://openalex.org/W3179652901","https://openalex.org/W4226272741","https://openalex.org/W7100070463","https://openalex.org/W7099421849","https://openalex.org/W1555903549","https://openalex.org/W2963126692"],"abstract_inverted_index":{"Let":[0],"$(M,\u03c9,\\mathcal{F}_1,\\mathcal{F}_2)$":[1],"be":[2],"a":[3,7,25,42,59,75],"bi-Lagrangian":[4,38,50,79,89,123],"manifold.":[5],"For":[6],"distribution":[8],"$\\mathcal{D}\\subseteq":[9],"TM$,":[10],"we":[11],"characterize":[12],"when":[13],"the":[14,19,30,48,54,98,106,115,119],"subbundle":[15],"$N^{*t}\\mathcal{D}:=\\mathcal{D}\\oplus":[16],"N^*\\mathcal{D}$":[17],"of":[18,44,105,118],"Whitney":[20],"sum":[21],"$W=TM\\oplus":[22],"T^*M$":[23],"is":[24],"Dirac":[26,46,69,83],"structure":[27,39],"for":[28],"both":[29,68],"untwisted":[31],"and":[32,81,94,96,103],"$(H,\u03b8)$-twisted":[33],"Courant":[34,82],"brackets.":[35],"Consequently,":[36],"every":[37],"canonically":[40],"determines":[41],"pair":[43],"transverse":[45],"structures.":[47,124],"associated":[49],"connection,":[51],"also":[52,86,110],"called":[53],"Hess":[55],"connection":[56,61],"$\\nabla$":[57],"induces":[58],"linear":[60],"on":[62,91,122],"$W$":[63],"with":[64],"respect":[65],"to":[66,112],"which":[67],"subbundles":[70],"are":[71],"parallel,":[72],"thereby":[73],"establishing":[74],"natural":[76],"link":[77],"between":[78,100],"geometry":[80],"geometry.":[84],"We":[85,109],"construct":[87],"induced":[88],"structures":[90],"$TM$,":[92],"$T^*M$,":[93],"$W$,":[95],"study":[97],"relation":[99],"their":[101],"affineness":[102],"that":[104],"original":[107],"structure.":[108],"lift":[111],"these":[113],"bundles":[114],"canonical":[116],"action":[117],"symplectomorphism":[120],"group":[121]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-07-15T00:00:00"}
