I need some help unraveling the terms that appear in the following passage. I found it in a book on some conference proceedings related to Differential Geometry.
Let $f:X \to R^3$ be a smooth curve with non-zero curvature where $X= \mathbb{S}^1 $ or $\mathbb{R}$.
Let $ Y(f) \subseteq Diff(X)$ be a subset of the set of diffeomorphisms on $X$ satisfying a certain property. Now if $A_1^3$ is the open Grassmannian of affine lines in $\mathbb{R}^3$, and if $N: X \to A_1^3$ is such that $N(x)$ is the normal at $x \in X$, then the non-zero curvature assures that $N$ is an immersion and this in turn shows that the group action $\phi : Y(f) \times X \to X$ is properly discontinuous.
Can anyone tell me how this is done and point me to some references on the results stated here??