This HTML5 document contains 59 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
dbohttp://dbpedia.org/ontology/
foafhttp://xmlns.com/foaf/0.1/
n12https://global.dbpedia.org/id/
dbthttp://dbpedia.org/resource/Template:
rdfshttp://www.w3.org/2000/01/rdf-schema#
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
owlhttp://www.w3.org/2002/07/owl#
n14https://archive.org/details/
wikipedia-enhttp://en.wikipedia.org/wiki/
dbchttp://dbpedia.org/resource/Category:
dbphttp://dbpedia.org/property/
provhttp://www.w3.org/ns/prov#
xsdhhttp://www.w3.org/2001/XMLSchema#
wikidatahttp://www.wikidata.org/entity/
dbrhttp://dbpedia.org/resource/

Statements

Subject Item
dbr:Quaternion
dbo:wikiPageWikiLink
dbr:Quaternionic_manifold
Subject Item
dbr:Quaternionic_analysis
dbo:wikiPageWikiLink
dbr:Quaternionic_manifold
Subject Item
dbr:Hyperkähler_manifold
dbo:wikiPageWikiLink
dbr:Quaternionic_manifold
Subject Item
dbr:Quaternionic_manifold
rdfs:label
Quaternionic manifold
rdfs:comment
In differential geometry, a quaternionic manifold is a quaternionic analog of a complex manifold. The definition is more complicated and technical than the one for complex manifolds due in part to the noncommutativity of the quaternions and in part to the lack of a suitable calculus of holomorphic functions for quaternions. The most succinct definition uses the language of G-structures on a manifold. Specifically, a quaternionic n-manifold can be defined as a smooth manifold of real dimension 4n equipped with a torsion-free -structure. More naïve, but straightforward, definitions lead to a dearth of examples, and exclude spaces like quaternionic projective space which should clearly be considered as quaternionic manifolds.
dcterms:subject
dbc:Differential_geometry dbc:Structures_on_manifolds dbc:Quaternions dbc:Manifolds
dbo:wikiPageID
56425908
dbo:wikiPageRevisionID
1053897908
dbo:wikiPageWikiLink
dbr:Algebra_over_a_field dbr:Whitney_sum dbr:Smooth_manifold dbr:Holomorphic_function dbr:Quaternion dbr:Differential_geometry dbc:Quaternions dbr:Section_(fiber_bundle) dbr:Noncommutative dbr:Sphere_bundle dbr:Torsion_tensor dbc:Structures_on_manifolds dbr:Complex_manifold dbr:Right_module dbr:Hypercomplex_manifold dbr:Quaternionic_vector_space dbr:Algebraic_geometry dbr:Endomorphism_bundle dbr:Quaternionic_matrix dbr:Quaternionic_Kähler_manifold dbr:Hyperkähler_manifold dbr:Almost_complex_structure dbr:Subbundle dbr:Quaternionic_projective_space dbr:Affine_connection dbr:Self-dual_manifold dbr:G-structure_on_a_manifold dbc:Manifolds dbr:Bundle_metric dbr:2-sphere dbr:Quaternions dbc:Differential_geometry
dbo:wikiPageExternalLink
n14:einsteinmanifold0000bess
owl:sameAs
n12:4WuqN wikidata:Q48816073
dbp:wikiPageUsesTemplate
dbt:Cite_book dbt:Manifolds
dbo:abstract
In differential geometry, a quaternionic manifold is a quaternionic analog of a complex manifold. The definition is more complicated and technical than the one for complex manifolds due in part to the noncommutativity of the quaternions and in part to the lack of a suitable calculus of holomorphic functions for quaternions. The most succinct definition uses the language of G-structures on a manifold. Specifically, a quaternionic n-manifold can be defined as a smooth manifold of real dimension 4n equipped with a torsion-free -structure. More naïve, but straightforward, definitions lead to a dearth of examples, and exclude spaces like quaternionic projective space which should clearly be considered as quaternionic manifolds.
prov:wasDerivedFrom
wikipedia-en:Quaternionic_manifold?oldid=1053897908&ns=0
dbo:wikiPageLength
8436
foaf:isPrimaryTopicOf
wikipedia-en:Quaternionic_manifold
Subject Item
dbr:Complex_manifold
dbo:wikiPageWikiLink
dbr:Quaternionic_manifold
Subject Item
dbr:Hypercomplex_manifold
dbo:wikiPageWikiLink
dbr:Quaternionic_manifold
Subject Item
dbr:Almost_quaternionic_manifold
dbo:wikiPageWikiLink
dbr:Quaternionic_manifold
dbo:wikiPageRedirects
dbr:Quaternionic_manifold
Subject Item
dbr:Almost_quaternionic_structure
dbo:wikiPageWikiLink
dbr:Quaternionic_manifold
dbo:wikiPageRedirects
dbr:Quaternionic_manifold
Subject Item
wikipedia-en:Quaternionic_manifold
foaf:primaryTopic
dbr:Quaternionic_manifold