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- Quaternion-Kähler_symmetric_space abstract "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 subgroupHere, 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-Kähler symmetric spaces are the homogeneous holomorphic contact manifolds, classified by Boothby: they are the adjoint varieties of the complex semisimple Lie groups.These spaces can be obtained 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 Kirillov-Kostant holomorphic symplectic form. This argument also explains how onecan associate a unique Wolf space to each of the simplecomplex Lie groups.".
- Quaternion-Kähler_symmetric_space wikiPageID "11018121".
- Quaternion-Kähler_symmetric_space wikiPageRevisionID "573359535".
- Quaternion-Kähler_symmetric_space subject Category:Differential_geometry.
- Quaternion-Kähler_symmetric_space subject Category:Homogeneous_spaces.
- Quaternion-Kähler_symmetric_space subject Category:Lie_groups.
- Quaternion-Kähler_symmetric_space subject Category:Riemannian_geometry.
- Quaternion-Kähler_symmetric_space subject Category:Structures_on_manifolds.
- Quaternion-Kähler_symmetric_space comment "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.".
- Quaternion-Kähler_symmetric_space label "Quaternion-Kähler symmetric space".
- Quaternion-Kähler_symmetric_space sameAs Quaternion-K%C3%A4hler_symmetric_space.
- Quaternion-Kähler_symmetric_space sameAs Q7269563.
- Quaternion-Kähler_symmetric_space sameAs Q7269563.
- Quaternion-Kähler_symmetric_space wasDerivedFrom Quaternion-Kähler_symmetric_space?oldid=573359535.