CHIRAL EQUATIONS AND FIBER-BUNDLES

Using the hypothesis g = g(lambda(i)), the chiral equations(rho-g,(z)g-1),zBAR+(rho-g,zBARg-1),z = 0 are reduced to a Killing equation of a p-dimensional space V(p), being lambda(i) = lambda(i)(z,zBAR) "geodesic" parameters of V(p). Supposing that g belongs to a Lie group G, one writes the corresponding Lie algebra elements (F) in terms of the Killing vectors of V(p) and the generators of the subalgebra of F of dimension d = dimension of the Killing space. The elements of the subalgebras belong to equivalence classes which in the respective group form a principal fiber bundle. This is used to integrate the matrix g in terms of the complex variables z and zBAR.