  We use hydrodynamic cosmological simulations to predict the star formation
properties of high-redshift galaxies (z=2-6) in five variants of the
inflationary cold dark matter scenario, paying particular attention to z=3, the
redshift of the largest "Lyman-break galaxy" (LBG) samples. Because we link the
star formation timescale to the local gas density, the rate at which a galaxy
forms stars is governed mainly by the rate at which it accretes cooled gas from
the surrounding medium. At z=3, star formation in most of the simulated
galaxies is steady on 200 Myr timescales, and the instantaneous star formation
rate (SFR) is correlated with total stellar mass. However, there is enough
scatter in this correlation that a sample selected above a given SFR threshold
may contain galaxies with a fairly wide range of masses. The redshift history
and global density of star formation in the simulations depend mainly on the
amplitude of mass fluctuations in the underlying cosmological model. The three
models whose mass fluctuation amplitudes agree with recent analyses of the
Lyman-alpha forest also reproduce the observed luminosity function of LBGs
reasonably well, though the dynamic range of the comparison is small and the
theoretical and observational uncertainties are large. The models with higher
and lower amplitudes appear to predict too much and too little star formation,
respectively, though they are not clearly ruled out. The intermediate amplitude
models predict SFR ~ 30-40 Msun/yr for galaxies with a surface density 1 per
arcmin^2 per unit redshift at z=3. They predict much higher surface densities
at lower SFR, and significant numbers of galaxies with SFR > 10 Msun/yr at z >=
5.
