  Based on the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory of
two-dimensional melting and the analogy between Laughlin states and the
two-dimensional one-component plasma (2DOCP), we investigate the possibility of
liquid crystalline states in a single Landau level (LL). We introduce many-body
trial wavefunctions that are translationally invariant but posess 2-fold (i.e.
{\em nematic}), 4-fold ({\em tetratic}) or 6-fold ({\em hexatic}) broken
rotational symmetry at respective filling factors $\nu = 1/3$, 1/5 and 1/7 of
the valence LL. We find that the above liquid crystalline states exhibit a soft
charge density wave (CDW) which underlies the translationally invariant state
but which is destroyed by quantum fluctuations. By means of Monte Carlo (MC)
simulations, we determine that, for a considerable variety of interaction
potentials, the anisotropic states are energetically unfavorable for the lowest
and first excited LL's (with index $L = 0, 1$), whereas the nematic is
favorable at the second excited LL ($L = 2$).
