  We have studied the Heisenberg antiferromagnets characterized by the magnetic
structures with the periods being two times larger than the lattice period. We
have considered all the types of the Bravais lattices (simple cubic, bcc and
fcc) and divided all these antiferromagnets into 7 classes i.e. 3 plus 4
classes denoted with symbols A and B correspondingly. The order parameter
characterizing the degeneracies of the magnetic structures is an ordinary Neel
vector for A classes and so-called 4-complex for B classes. We have taken into
account the fluctuation corrections for these states within the spin-wave and
large-N expansions ($N$ is the number of spin components). Below the Neel
temperature $T_{\rm{N}}$ quantum and thermal fluctuations lift the degeneracy
making simple one-wave vector collinear structure preferable for all the
classes. A satellite of this effect is opening of the exchange gaps at certain
wave vectors in the spin wave spectrum (there is an analogous effect for the
nonuniform static transverse susceptibility). However, as the temperature
approaches $T_{\rm{N}}$, the exchange gaps are closing. We have calculated the
critical indices $\eta$ and $\nu$ to order of $1/N$ and found that they differ
for A and B classes.
