We show asymptotically and numerically that a constant-density flame will exhibit different geometrical shapes which depend on the flow time-scales. In particular, a frozen flow may yield a flame surface composed of bulges connected by cusps, whereas a pulsating flow may dampen the flame motion to the extent that only a flat, laminar flame surface will be possible. The cusp nature disappears when the eddy frequency becomes comparable touLk, whereuLis the laminar flame speed and k is a characteristic wave number of the flow. Flame shapes obtained with a sheet of laser light within a spark-ignited engine show a cusp nature only at low engine RPM, in agreement with the frequency criteria given above.