Editing Isometry (section)

===Properties===
A collection of isometries typically form a group, the [[isometry group]]. When the group is a [[continuous group]], the [[Lie group|infinitesimal generators]] of the group are the [[Killing vector field]]s. 

The [[Myers–Steenrod theorem]] states that every isometry between two connected Riemannian manifolds is smooth (differentiable). A second form of this theorem states that the isometry group of a Riemannian manifold is a [[Lie group]].

[[Symmetric space]]s are important examples of [[Riemannian manifold]]s that have isometries defined at every point.