About: Quaternionic manifold

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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.

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rdfs:label	Quaternionic manifold (en)
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. (en)
dcterms:subject	Differential geometry Structures on manifolds Manifolds Quaternions
Wikipage page ID	56425908 (xsd:integer)
Wikipage revision ID	1053897908 (xsd:integer)
Link from a Wikipage to another Wikipage	Quaternion Algebra over a field Holomorphic function Hyperkähler manifold Right module Quaternions Differential geometry Structures on manifolds Quaternionic projective space Quaternionic vector space Complex manifold 2-sphere Whitney sum G-structure on a manifold Affine connection Algebraic geometry Manifolds Quaternions Hypercomplex manifold Torsion tensor Differential geometry Bundle metric Endomorphism bundle Section (fiber bundle) Smooth manifold Noncommutative Subbundle Quaternionic matrix Sphere bundle Quaternionic Kähler manifold Almost complex structure dbr:Self-dual_manifold
Link from a Wikipage to an external page	https://archive.org/details/einsteinmanifold0000bess
sameAs	Quaternionic manifold Quaternionic manifold
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Manifolds
has 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. (en)
prov:wasDerivedFrom	wikipedia-en:Quaternionic_manifold?oldid=1053897908&ns=0
page length (characters) of wiki page	8436 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Quaternionic_manifold
is Link from a Wikipage to another Wikipage of	Quaternion Quaternionic analysis Hyperkähler manifold Complex manifold Hypercomplex manifold Almost quaternionic manifold Almost quaternionic structure
is Wikipage redirect of	Almost quaternionic manifold Almost quaternionic structure
is foaf:primaryTopic of	wikipedia-en:Quaternionic_manifold

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