Homogeneous HKT and QKT manifolds

1998/07/24 by A. Opfermann, G. Papadopoulos, Opfermann, A. +1 · 1 citation
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/9807026

latex2e, 33 pages, 2 figures

arxiv created 1998/07/24 · arxiv updated 2009/11/30

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.

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