Abstract:
For each compact Lie algebra ? and each real representation V of ? we consider a two-step nilpotent Lie group N(?,V), endowed with a natural left-invariant riemannian metric. The homogeneous nilmanifolds so obtained are precisely those which are naturally reductive. We study some geometric aspects of these manifolds, finding many parallels with H-type groups. We also obtain, within the class of manifolds N(?,V), the first examples of non-weakly symmetric, naturally reductive spaces and new examples of non-commutative naturally reductive spaces.
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Received: 16 September 1998 / Revised version: 24 February 1999
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Lauret, J. Homogeneous nilmanifolds attached to representations of compact Lie groups. manuscripta math. 99, 287–309 (1999). https://doi.org/10.1007/s002290050174
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DOI: https://doi.org/10.1007/s002290050174