Journal of the
Korean Mathematical Society JKMS

Let $G$ be the 3-dimensional Heisenberg group. A discrete subgroup of $\isom(G)$, %the isometry group of $G$ acting freely on $G$ with non-compact quotient, must be isomorphic to either 1, $\bbz$, $\bbz^2$ or the fundamental group of the Klein bottle. We classify all discrete representations of such groups into $\isom(G)$ up to affine conjugacy. This yields an affine classification of 3-dimensional non-compact infra-nilmanifolds.

Keywords: infranil-manifolds, almost flat manifolds, Heisenberg group

MSC numbers: Primary 57R15, 57S25, 57S10; Secondary 53C30