Projective differential geometry of higher reductions of the two-dimensional Dirac equation (Q556223)

The authors discuss reductions of the 2-dimensional Dirac equation and their relations with projective differential geometry: 2nd order reductions and the geometry of line congruences in 3-dimensional projective space lying in linear complexes (Sect.~2); 3rd order reductions and the geometry of isotropic line congruences in 5-dimensional projective space (Sect.~3); and reductions in the framework of the multicomponent KP hirarchy (Sect.~4). Background material on Wilczynski's approach to surfaces in projective geometry and on W-congruences is included in two appendices. The paper does not contain any theorems.