  Let $G$ be a reductive algebraic group over an algebraically closed field $k$
of characteristic $p>0$, and assume $p$ is good for $G$. Let $P$ be a parabolic
subgroup with unipotent radical $U$. For $r \ge 1$, denote by
$\mathbb{G}_{a(r)}$ the $r$-th Frobenius kernel of $\mathbb{G}_a$. We prove
that if the nilpotence class of $U$ is less than $p$, then any embedding of
$\mathbb{G}_{a(r)}$ in $U$ lies inside a one-parameter subgroup of $U$, and
there is a canonical way in which to choose such a subgroup. Applying this
result, we prove that if $p$ is at least as big as the Coxeter number of $G$,
then the cohomological variety of $G_{(r)}$ is homeomorphic to the variety of
$r$-tuples of commuting elements in $\mathcal{N}_1(\mathfrak{g})$, the
$[p]$-nilpotent cone of $Lie(G)$.
