  Koras-Russell threefolds are certain smooth contractible complex
hypersurfaces in affine complex four-space which are not algebraically
isomorphic to affine three-space. One of the important examples is the cubic
Russell threefold, defined by the equation x^2y+z^2+t^3+x=0. In a previous
article by A. Dubouloz, P.M. Poloni and the author, the automorphism group of
the Russell cubic threefold was studied. It was shown, in particular, that all
automorphisms of this hypersurface extend to automorphisms of the ambient
space. This has several interesting consequences, including the fact that one
can find another hypersurface which is isomorphic to the Russell cubic, but
such that the two hypersurfaces are inequivalent. In the present article, we
will discuss how some of these results can be generalized to the class of
Koras-Russell threefolds of the first kind.
