On Separable ${\text{A}}^2$ and ${\text{A}}^3$-forms

In this paper, we will prove that any ${\text{A}}^3$-form over a field $k$ of characteristic zero is trivial provided it has a locally nilpotent derivation satisfying certain properties. We will also show that the result of T. Kambayashi on the triviality of separable ${\text{A}}^2$-forms over a field $k$ extends to ${\text{A}}^2$-forms over any one-dimensional Noetherian domain containing $\text{bQ}$.