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.
On the Riemannian Geometry of the Nilpotent groups H(p,r)
PIU, MARIA PAOLA;
1993-01-01
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.
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