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• W3101471031 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." @default.
• W3101471031 created "2020-11-23" @default.
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• W3101471031 date "2002-01-22" @default.
• W3101471031 modified "2023-10-14" @default.
• W3101471031 title "HyperKähler torsion structures invariant by nilpotent Lie groups" @default.
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• W3101471031 doi "https://doi.org/10.1088/0264-9381/19/3/309" @default.
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