Extension Problem for Flexible Varieties

We consider n - dimensional, with n greater or equal to 4, flexible quasi-affine varieties X, that are varieties on which the group generated by all one-parameter unipotent subgroups of Aut(X) acts transitively. We prove that for any subvariety Y of X, isomorphic to a line, every SL(n) - automorphism of the normal bundle of Y is induced by a global automorphism of X. We also extend this result also to automorphisms of jet bundles on Y.