DEGENERATE TORSION-FREE G3-CONNECTIONS

Using exterior differential systems (EDS), Bryant proved that the moduli space of nondegenerate analytic torsion-free G3-connections depends on four functions in three variables. Here nondegeneracy is a technical condition which imposes the nonvanishing everywhere of a certain determinant pertinent to a torsion-free G3-connection for EDS to carry through. The finite-dimensional moduli of homogeneous torsion-free G3-connections are degenerate examples, where the determinant vanishes identically. We establish in fact that the moduli space of analytic inhomogeneous degenerate torsion-free G3-connections is infinite-dimensional.