Rational curves and prolongations of G-structures

Abstract

In a joint work with N. Mok in 1997, we proved that for an irreducible representation $G \subset {\bf GL}(V),$ if a holomorphic $G$-structure exists on a uniruled projective manifold, then the Lie algebra of $G$ has nonzero prolongation. We tried to generalize this to an arbitrary connected algebraic subgroup $G \subset {\bf GL}(V)$ and a complex manifold containing an immersed rational curve, but the proposed proof had a flaw.