Using four-point magnetic field measurements by the Cluster spacecraft, we statistically analyze the magnetic field and electric current configurations during rapid crossings of the current sheet observed in July-October 2001 at geocentric distances of 19 R_E. The database includes 78 crossings, specially selected to apply multi-point data analysis techniques to calculate vector derivatives. Observed bipolar variations of j_z, often with j_z > j_y, indicate that the electric currents follow kinks of the current sheet. The current density varies between 5-25 nA/m². The half-thickness of the current sheet during flapping varies over a wide range, from 1 to 20 ion thermal gyroradii (L_cp, calculated from average temperature and lobe magnetic field for each crossing). We found no relationship between the tilt angle of the current sheet normal and the half-thickness. In 68 cases the magnetic field curvature vector has a positive (earthward) X-component. Ten cases with a negative (tailward) curvature, associated with reconnection, were detected within 0<Y_GSM<7 R_E. The minimum curvature radii vary mainly between 1 and 10 L_cp, and the adiabaticity parameter K≤1 for 73% of the events. The electric current density during flapping is often off-central, i.e. the main current density is shifted from the neutral sheet ( B_x, <5 nT) to the Northern or Southern Hemisphere. This is most likely a temporal effect related to the flapping. The analysis shows that the flapping motion of the current sheet is associated with kink-like waves on the sheet surface. The kink fronts, tilted in the Y - Z plane, moved toward dawn in the morning half and toward dusk in the evening half of the magnetotail.