  We have studied the Heisenberg antiferromagnets on two-dimensional frustrated
lattices, triangular and kagome lattices using linear spin-wave theory. A
collinear ground state ordering is possible if one of the three bonds in each
triangular plaquette of the lattice becomes weaker or frustrated. We study
spiral order in the Heisenberg model along with Dzyaloshinskii-Moriya (DM)
interaction and in the presence of a magnetic field. The quantum corrections to
the ground state energy and sublattice magnetization are calculated
analytically in the case of triangular lattice with nearesr-neighbour
interaction. The corrections depend on the DM interaction strength and the
magnetic field. We find that the DM interaction stabilizes the long-range
order, reducing the effect of quantum fluctuations. Similar conclusions are
reached for the kagome lattice. We work out the linear spin-wave theory at
first with only nearest-neighbour (nn) terms for the kagome lattice. We find
that the nn interaction is not sufficient to remove the effects of low energy
fluctuations. The flat branch in the excitation spectrum becomes dispersive on
addition of furthet neighbour interactions. The ground state energy and the
excitation spectrum have been obtained for various cases.
