About: Quaternion-Kšhler symmetric space     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:Group100031264, within Data Space : dbpedia.org associated with source document(s)
QRcode icon
http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FQuaternion-Kähler_symmetric_space

In differential geometry, a quaternion-Kähler symmetric space or Wolf space is a quaternion-Kähler manifold which, as a Riemannian manifold, is a Riemannian symmetric space. Any quaternion-Kähler symmetric space with positive Ricci curvature is compact and simply connected, and is a Riemannian product of quaternion-Kähler symmetric spaces associated to compact simple Lie groups. For any compact simple Lie group G, there is a unique G/H obtained as a quotient of G by a subgroup

AttributesValues
rdf:type
rdfs:label
  • Quaternion-K√§hler symmetric space
rdfs:comment
  • In differential geometry, a quaternion-K√§hler symmetric space or Wolf space is a quaternion-K√§hler manifold which, as a Riemannian manifold, is a Riemannian symmetric space. Any quaternion-K√§hler symmetric space with positive Ricci curvature is compact and simply connected, and is a Riemannian product of quaternion-K√§hler symmetric spaces associated to compact simple Lie groups. For any compact simple Lie group G, there is a unique G/H obtained as a quotient of G by a subgroup
foaf:isPrimaryTopicOf
dct:subject
Wikipage page ID
Wikipage revision ID
Link from a Wikipage to another Wikipage
sameAs
dbp:wikiPageUsesTemplate
has abstract
  • In differential geometry, a quaternion-K√§hler symmetric space or Wolf space is a quaternion-K√§hler manifold which, as a Riemannian manifold, is a Riemannian symmetric space. Any quaternion-K√§hler symmetric space with positive Ricci curvature is compact and simply connected, and is a Riemannian product of quaternion-K√§hler symmetric spaces associated to compact simple Lie groups. For any compact simple Lie group G, there is a unique G/H obtained as a quotient of G by a subgroup Here, Sp(1) is the compact form of the SL(2)-triple associated with the highest root of G, and K its centralizer in G. These are classified as follows. The twistor spaces of quaternion-K√§hler symmetric spaces are the homogeneous holomorphic contact manifolds, classified by Boothby: they are the of the complex semisimple Lie groups. These spaces can be obtained by taking a projectivization ofa minimal nilpotent orbit of the respective complex Lie group.The holomorphic contact structure is apparent, becausethe nilpotent orbits of semisimple Lie groups are equipped with the holomorphic symplectic form. This argument also explains how onecan associate a unique Wolf space to each of the simplecomplex Lie groups.
prov:wasDerivedFrom
page length (characters) of wiki page
is foaf:primaryTopic of
is Link from a Wikipage to another Wikipage of
is Wikipage redirect of
is Wikipage disambiguates of
Faceted Search & Find service v1.17_git51 as of Sep 16 2020


Alternative Linked Data Documents: PivotViewer | iSPARQL | ODE     Content Formats:       RDF       ODATA       Microdata      About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 08.03.3319 as of Dec 29 2020, on Linux (x86_64-centos_6-linux-glibc2.12), Single-Server Edition (61 GB total memory)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2021 OpenLink Software