  We investigate antiferromagnetic spin chains, which are coupled by a weak
antiferromagnetic exchange interaction on a hexagonal lattice. We particulary
study the role of the dipole-dipole interaction within the framework of a
Heisenberg model with nearest-neighbor exchange and additional dipolar
interaction. We find several commensurate and incommensurate phases depending
on the ratio of dipolar energy to interchain-exchange energy due to their
competing qualtity. The ground-state analysis is supplemented by a stability
analysis by means of a linear spin-wave theory. In comparison with experiments
(CsMnBr_3, RbMnBr_3) we obtain good agreement for the energy gaps. From this we
conclude, that the dipolar interaction is the most important source of
anisotropy in these Mn-compounds.
