Homogeneous HKT and QKT manifolds

Details Homogeneous HKT and QKT manifolds Homogeneous HKT and QKT manifolds

1998-07-24

arxiv.org/abs/math-ph/9807026v1

Physics

Mathematical Physics

latex2e, 33 pages, 2 figures

Scientific paper

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.

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