The HKT manifolds (HKT stands for Hyper-Kahler with torsion) are the complex manifolds of dimension 4n which admit a triple of complex structures that satisfy the quaternionic algebra and are covariantly constant with respect to one and the same torsionful Bismut connection. In contrast to compact hyper-Kahler manifolds that are rather rare and dicult to construct, compact HKT manifolds are rather abundant. In particular, many group manifolds G and homogeneous spaces G=H of dimension 4n enjoy HKT geometry.
I present a new simple proof of this fact based on the observation that the dierent complex structures are interrelated by automorphisms of the Lie algebra g.
(Based on [A.S., Nucl. Phys. B 957 (2020) 115052].)
HKT manifolds
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Nom de l'orateur
Andrei Smilga
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SUBATECH
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