  In this paper we study quasiconformal curves which are a special case of
quasiregular curves. Namely embeddings $\Omega\rightarrow\mathbb{R}^m$ from
some domain $\Omega\subset\mathbb{R}^n$ to $\mathbb{R}^m$, where $n\leq m$,
which belong in a suitable Sobolev class and satisfy a certain distortion
inequality for some smooth, closed and non-vanishing $n$-form in
$\mathbb{R}^m$. These mappings can be seen as quasiconformal mappings between
$\Omega$ and $f(\Omega)$. We prove that a quasiconformal curve always satisfies
the analytic definition of quasiconformal mappings and the lower half of the
modulus inequality. Moreover, we give a sufficient condition for a
quasiconformal curve to satisfy the metric definition of quasiconformal
mappings. We also show that a quasiconformal map from $\Omega$ to
$f(\Omega)\subset \mathbb{R}^m$ is a quasiconformal $\omega$ curve for some
form $\omega$ under suitable assumptions. Finally, we show the same is true
when we equip the target space $f(\Omega)$ with its intrinsic metric instead of
the Euclidean one.
