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manuscripta mathematica

, Volume 99, Issue 3, pp 287–309 | Cite as

Homogeneous nilmanifolds attached to representations of compact Lie groups

  • Jorge Lauret

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.

Mathematics Subject Classification (1991): Primary 22E25, 43A20; Secondary 22E30, 53C30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Jorge Lauret
    • 1
  1. 1.FaMAF, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina.¶e-mail: lauret@mate.uncor.eduUS

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