  The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic
nearest, $J_1=-(1-p)J,$ $J>0$, and antiferromagnetic third-nearest-neighbor,
$J_3=pJ$, exchange interactions is studied in the range of the parameter $0
\leqslant p \leqslant 1$. Mori's projection operator technique is used as a
method, which retains the rotation symmetry of spin components and does not
anticipate any magnetic ordering. For zero temperature several phase
transitions are observed. At $p\approx 0.2$ the ground state is transformed
from the ferromagnetic spin structure into a disordered state, which in its
turn is changed to an antiferromagnetic long-range ordered state with the
incommensurate ordering vector ${\bf Q = Q^\prime} \approx (1.16, 0)$ at
$p\approx 0.31$. With the further growth of $p$ the ordering vector moves along
the line ${\bf Q^\prime-Q_c}$ to the commensurate point ${\bf
Q_c}=(\frac{2\pi}{3}, 0)$, which is reached at $p = 1$. The final state with an
antiferromagnetic long-range order can be conceived as four interpenetrating
sublattices with the $120^\circ$ spin structure on each of them. Obtained
results are used for interpretation of the incommensurate magnetic ordering
observed in NiGa$_2$S$_4$.
