Riser pipe with rigid auxiliary lines

A riser comprising at least two riser sections assembled end to end, each of the riser sections comprising a main tube, at least one auxiliary line element arranged substantially parallel to said main tube, a connector connecting adjacent ends of the main tubes of the at least two riser sections, the connector allowing longitudinal tensional stresses to be transmitted from the main tube of one of the riser sections to the main tube of an adjacent riser section, and a linking connector connecting adjacent ends of the auxiliary line elements of the at least two riser sections, the linking connector allowing longitudinal tensional stresses to be transmitted from the auxiliary line element of one of the riser sections to the auxiliary line element of the adjacent riser sections, wherein the linking connector comprises a male tubular element and a female tubular element that fit into one another and have an axial shoulder for longitudinal positioning of the male tubular element in relation to the female tubular element, a locking ring mounted mobile in rotation on one of the tubular elements, the locking ring comprising studs that cooperate with the studs of the other tubular element so as to form a bayonet joint.