Direct numerical simulations (DNS) are ideally suited to investigate in detail turbulent reacting flows in simple geometries. When considering such problems as pollutant emission or stability limits, detailed models must generally be employed to describe the chemical processes with sufficient accuracy. Due to the huge cost of such simulations, they have been mostly restricted to two-dimensional configurations up to now, leading to unsolved questions concerning the generality of the obtained results. We have recently developed a three-dimensional DNS code leading to reasonable computing times, thanks to the low-Mach- number approximation and to a new chemistry reduction technique. This code is used here to investigate the evolution of premixed methane/air flame kernels placed in a homogeneous isotropic turbulence field. This situation typifies the initial flame development after spark ignition in a gas turbine or an internal combustion engine. Laminar reference computations are carried out in one and two dimensions and are compared with turbulent results obtained in two and three dimensions. Evolution of flame surface area, stretch rate, and flame front curvature are in particular presented and show considerable differences between two-dimensional and three-dimensional computations. The interest of repeating the computations to increase the statistical validity of the results is demonstrated in two dimensions, but is not sufficient to explain the discrepancy obtained with the three-dimensional computation. Further three-dimensional sim- ulations are nevertheless needed to quantify more precisely the observed changes (slower increase of the equivalent radius, higher stretch rate, and curvature shifted toward positive values).