  Using the classical density functional theory of freezing and Monte Carlo
computer simulations, we explore the liquid-crystalline phase behavior of hard
rectangles on flat and cylindrical manifolds. Moreover, we study the effect of
a static external field which couples to the rectangles' orientations, aligning
them towards a preferred direction. In the flat and field-free case, the bulk
phase diagram involves stable isotropic, nematic, tetratic, and smectic phases
depending on the aspect ratio and number density of the particles. The external
field shifts the transition lines significantly and generates a binematic phase
at the expense of the tetratic phase. On a cylindrical manifold, we observe
tilted smectic-like order, as obtained by wrapping a smectic layer around a
cylinder. We find in general good agreement between our density functional
calculations and particle-resolved computer simulations and mention possible
setups to verify our predictions in experiments.
