  We prove that curves of constant curvature satisfy the parametric $C^1$-dense
relative $h$-principle in the space of immersed curves with nonvanishing
curvature in Euclidean space $R^{n\geq 3}$. It follows that two knots of
constant curvature in $R^3$ are isotopic, resp. homotopic, through curves of
constant curvature if and only if they are isotopic, resp. homotopic, and their
self-linking numbers, resp. self-linking numbers mod $2$, are equal.
