On the Riemannian Geometry of the Nilpotent groups H(p,r)

PIU, MARIA PAOLA;GOZE MICHEL

1993-01-01

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Abstract

We study some aspect of the left-invariant Riemannian geometry on a class of nilpotent Lie groups H(p, r) that generalize the Heisenberg group H2p+1. Let us prove that the groups of type H (or Kaplan's spaces) and the H(p, r) groups have same common Riemannian properties but they are not the same spaces.