A premixing burner on the double-cone principle consists essentially of two hollow conical partial bodies (111, 112) which are interleaved in the flow direction and whose respective center lines (113, 114) are offset relative to one another. The adjacent walls of the two partial bodies form tangential gaps (20) in their longitudinal extent for the combustion air. Gas inlet openings (117) distributed in the longitudinal direction are provided in the walls of the two partial bodies. The air is guided into the tangential gaps (20) via vortex generators (9) of which a plurality are arranged adjacent to one another. The fuel is introduced into the gaps (20) in the immediate region of the vortex generators (9).Using the novel static mixer which the three-dimensional vortex generators represent, longitudinal vortices without recirculation region can be generated in the inlet gap through which flow occurs. It is therefore possible to achieve extraordinarily short mixing distances at the inlet to the burner with a small pressure loss at the same time.