Homogeneous HKT and QKT manifolds

Abstract

We present the construction of a large class of homogeneous KT, HKT and QKT manifolds, $G/K$, using an invariant metric on $G$ and the canonical connection. For this a decomposition of the Lie algebra of $G$ is employed, which is most easily described in terms of colourings of Dynkin diagrams of simple Lie algebras. KT structures on homogeneous spaces are associated with different colourings of Dynkin diagrams. The colourings which give rise to HKT structures are found using extended Dynkin diagrams. We also construct homogeneous QKT manifolds from homogeneous HKT manifolds and show that their twistor spaces admit a KT structure. Many examples of homogeneous KT, HKT and QKT spaces are given.

latex2e, 33 pages, 2 figures

Cited by in corpus (9)

• Geometry of Hyper-Kähler Connections with Torsion
• Geometry of Quaternionic Kähler connections with torsion
• An Index for 2D field theories with large N=4 superconformal symmetry
• Instantons on sine-cones over Sasakian manifolds
• Positive toric fibrations
• Homogeneous Einstein metrics on non-Kähler C-spaces
• Group manifolds and homogeneous spaces with HKT geometry: the role of automorphisms
• Homogeneous Hypercomplex Structures and the Joyce's Construction
• A Moduli Space of the Quaternionic Hopf Surface Encodes Standard Model Physics