FFINE THREEFOLDS WITH $$ \mathbb{} $$2-FIBRTIONS

An affine threefold containing an \( \mathbb{A} \) 2-cylinder is studied. The existence of \( \mathbb{A} \) 2-cylinders is almost equivalent to the existence of mutually commuting, independent Ga-actions σ1, σ2. A typical example of such affine threefolds is a hypersurface x m y = f(x, z, t), and we generalize such a hypersurface to define an affine pseudo-3-space. After I. Heden [He], we observe also a Ga-action on the hypersurface x m y = f(x, z, t) with m ≥ 2.