  We provide a Reifenberg type characterization for $m$-dimensional
$C^1$-submanifolds of $\mathbb R^n$. This characterization is also equivalent
to Reifenberg-flatness with vanishing constant combined with suitably
converging approximating $m$-planes. Moreover, a sufficient condition can be
given by the finiteness of the integral of the quotient of $\theta(r)$-numbers
and the scale $r$, and examples are presented to show that this last condition
is not necessary.
