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$\mathbb{A}^{2}$
AND 
$\mathbb{A}^{3}$
-FORMS
$\mathbb{A}^{3}$
-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 Kambayashi on the triviality of separable 
$\mathbb{A}^{2}$
-forms over a field 
$k$
extends to 
$\mathbb{A}^{2}$
-forms over any one-dimensional Noetherian domain containing 
$\mathbb{Q}$
.