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Hyperkähler torsion structures invariant by nilpotent Lie groups

Isabel G. Dotti·Anna Fino
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Abstract

We study HKT structures on nilpotent Lie groups and on associated nilmanifolds. We exhibit three weak HKT structures on $\R^8$ which are homogeneous with respect to extensions of Heisenberg type Lie groups. The corresponding hypercomplex structures are of a special kind, called abelian. We prove that on any 2-step nilpotent Lie group all invariant HKT structures arise from abelian hypercomplex structures. Furthermore, we use a correspondence between abelian hypercomplex structures and subspaces of ${\frak sp}(n)$ to produce continuous families of compact and noncompact of manifolds carrying non isometric HKT structures. Finally, geometrical properties of invariant HKT structures on 2-step nilpotent Lie groups are obtained.

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Isabel G. Dotti, Anna Fino. 2001-12-17. Hyperkähler torsion structures invariant by nilpotent Lie groups. https://doi.org/10.1088/0264-9381%2F19%2F3%2F309

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