Examples of isometry

isometry isn’t in the Cambridge Dictionary yet. You can help!
If f is biholomorphic, then it is a global isometry.
The present paper goes further and shows that the resistance and resistance dimension are invariant under rough isometry between graphs.
Any system of isometries can be decomposed into minimal components and finite orbits in a certain way.
On the rigidity of discrete isometry groups of negatively curved spaces.
On the geometry of orientation preserving planar piecewise isometries.
Tangencies in invariant disk packings for certain planar piecewise isometries are rare.
It follows that the function is constant and that is an isometry of the plane.
The homothety is an isometry since lengths of closed geodesics are the same.
This was the case with rough isometry as well.
In this note it is shown that resistance and resistance dimension are rough isometry invariant.
The geodesic convexity is preserved by isometries, and by taking finite intersections.
We apply this to the isometry problem of rigid geometric structures.
On conditions under which isometries have bounded orbits.
Then any two points in the limit set can be approximated by the fixed points of some hyperbolic isometry.
From this, we may conclude easily that diabolicity is quasi-isometry invariant among uniformly locally finite graphs.

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