About: Quaternion-Kähler manifold

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In differential geometry, a quaternion-Kähler manifold (or quaternionic Kähler manifold) is a Riemannian 4n-manifold whose Riemannian holonomy group is a subgroup of Sp(n)·Sp(1) for some . Here Sp(n) is the sub-group of consisting of those orthogonal transformations that arise by left-multiplication by some quaternionic matrix, while the group of unit-length quaternions instead acts on quaternionic -space by right scalar multiplication. The Lie group generated by combining these actions is then abstractly isomorphic to .

Attributes	Values
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rdfs:label	Quaternionische Kähler-Mannigfaltigkeit (de) 사원수 켈러 다양체 (ko) Quaternion-Kähler manifold (en)
rdfs:comment	In der Mathematik sind quaternionische Kähler-Mannigfaltigkeiten ein Forschungsgebiet der Differentialgeometrie. (de) 미분기하학에서 사원수 켈러 다양체(영어: quaternion-Kähler manifold)는 홀로노미가 Sp(n)×Sp(1)인 리만 다양체다. (ko) In differential geometry, a quaternion-Kähler manifold (or quaternionic Kähler manifold) is a Riemannian 4n-manifold whose Riemannian holonomy group is a subgroup of Sp(n)·Sp(1) for some . Here Sp(n) is the sub-group of consisting of those orthogonal transformations that arise by left-multiplication by some quaternionic matrix, while the group of unit-length quaternions instead acts on quaternionic -space by right scalar multiplication. The Lie group generated by combining these actions is then abstractly isomorphic to . (en)
dcterms:subject	Structures on manifolds Manifolds Riemannian geometry
Wikipage page ID	2640559 (xsd:integer)
Wikipage revision ID	1084926517 (xsd:integer)
Link from a Wikipage to another Wikipage	Scalar curvature Alfred Gray (mathematician) Almost complex manifold Hyperkähler manifold Joseph A. Wolf Kähler–Einstein metric Structures on manifolds Quaternionic projective space Quaternion-Kähler symmetric space Manifolds Edmond Bonan Fano variety Riemannian geometry Einstein manifold Holonomy Differential geometry Marcel Berger Sasakian manifold Hyperkähler Centralizer Contact manifold Locally symmetric Wolf space dbr:Vivian_Kraines
Link from a Wikipage to an external page	https://books.google.com/books%3Fid=aVUjiBNCyogC https://books.google.com/books%3Fid=c3P-YUD8GZQC
sameAs	Quaternion-Kähler manifold Quaternion-Kähler manifold Quaternion-Kähler manifold Quaternion-Kähler manifold Quaternion-Kähler manifold
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Refbegin dbt:Harvid
has abstract	In der Mathematik sind quaternionische Kähler-Mannigfaltigkeiten ein Forschungsgebiet der Differentialgeometrie. (de) In differential geometry, a quaternion-Kähler manifold (or quaternionic Kähler manifold) is a Riemannian 4n-manifold whose Riemannian holonomy group is a subgroup of Sp(n)·Sp(1) for some . Here Sp(n) is the sub-group of consisting of those orthogonal transformations that arise by left-multiplication by some quaternionic matrix, while the group of unit-length quaternions instead acts on quaternionic -space by right scalar multiplication. The Lie group generated by combining these actions is then abstractly isomorphic to . Although the above loose version of the definition includes hyperkähler manifolds, the standard convention of excluding these will be followed by also requiring that the scalar curvature be non-zero— as is automatically true if the holonomy group equals the entire group Sp(n)·Sp(1). (en) 미분기하학에서 사원수 켈러 다양체(영어: quaternion-Kähler manifold)는 홀로노미가 Sp(n)×Sp(1)인 리만 다양체다. (ko)
prov:wasDerivedFrom	wikipedia-en:Quaternion-Kähler_manifold?oldid=1084926517&ns=0
page length (characters) of wiki page	10729 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Quaternion-Kähler_manifold
is Link from a Wikipage to another Wikipage of	Quaternionic Kaehler manifold List of differential geometry topics Hyperkähler manifold Ricci-flat manifold Quaternion-Kaehler Quaternion-Kaehler manifold Quaternion-Kahler Quaternion-Kahler manifold Quaternion Kaehler manifold Quaternionic-Kaehler manifold Quaternionic-Kahler manifold Calibrated geometry Quaternion-Kähler symmetric space Erich Kähler Edmond Bonan Holonomy Marcel Berger Kähler manifold Quaternion-Kähler Quaternion Kahler manifold Quaternion Kähler manifold Quaternionic-Kähler manifold Quaternionic Kahler manifold Quaternionic Kähler manifold
is Wikipage redirect of	Quaternionic Kaehler manifold Quaternion-Kaehler Quaternion-Kaehler manifold Quaternion-Kahler Quaternion-Kahler manifold Quaternion Kaehler manifold Quaternionic-Kaehler manifold Quaternionic-Kahler manifold Quaternion-Kähler

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