ON A 2-DIMENSIONAL DARBOUX SYSTEM - INTEGRABLE AND GEOMETRIC CONNECTIONS(1)

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 versio n yields a classical system investigated by Darboux in connection with conjugate coordinate systems. This Darboux system, in a 1 + 1-dimensi onal reduction, turns out to be connected to the self-induced transpar ency equations. Here, geometric aspects of the 2 + 1-dimensional Darbo ux systems are recorded.