On a 2 + 1-dimensional Darboux system: Integrable and geometric connections

It is shown that a novel 2 + 1-dimensional system recently introduced by Konopelchenko and Rogers contains as a specialization the Zakharov-Manakov matrix triad system. The latter, in turn, in its scalar version yields a classical system investigated by Darboux in connection with conjugate coordinate systems. This Darboux system, in a 1 + 1-dimensional reduction, turns out to be connected to the self-induced transparency equations. Here, geometric aspects of the 2 + 1-dimensional Darboux systems are recorded.