  We investigate analytically and numerically the classical ground states of
frustrated Heisenberg models on pyrochlore and kagome lattices in zero and
finite magnetic fields. Each model has a wide region in the microscopic
parameter space, where the propagation vector is turned to a commensurate
position equal to a half of the reciprocal lattice vector with a nontrivial
star. Within these regions the zero-field ground states for both models
correspond to noncoplanar triple-k spin configurations. A universal appearance
of the 3-k states can be related to the spin-space dimensionality. A strong
magnetic field freezes the longitudinal spin component reducing the spin-space
dimensionality. Accordingly, we find transitions into the double-k magnetic
structures induced by applied field for both spin models. The predicted
transition between 3-k and 2-k states may explain the hitherto unexplained
transitions observed experimentally in cubic spinels GeNi2O4 and GeCo2O4 under
magnetic field.
