ON THE RUSSELL-KORAS CONTRACTILE THREEFOLDS

P. Russell and M. Koras classified all smooth affine contractible thre efolds with hyperbolic C-action and quotient isomorphic to that of th e corresponding linear action on the tangent space at the unique fixed point. It is not clear from their description whether there exist non trivial Russell-Koras threefolds that are isomorphic to C-3. They show ed that this question arises naturally in connection with the problem of linearizing a C-action on C-3. We prove that none of the nontrivia l Russell-Koras threefolds are isomorphic to C-3.