New answers tagged isometry
4
votes
Exercise 2.6 in Katok's book "Fuchsian Groups"
Here is a counter-example to the implication (iii)$\Rightarrow$(i). Consider $\mathbb R$ with the metric
$$
d(x,y)=\min\{ |x-y|, 1\}.
$$
Let $X=\mathbb R\times \{0,1\}$ denote the disjoint union of ...
- 105k
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vote
Rigid motion vs Isometry
In the sense of differential geometry of surfaces, isometries and rigid motions are different.
Every rigid motion is an isometry, but not the opposite. Isometry preserves the first fundamental form ...
- 2,040
0
votes
Accepted
Isometries and Isomorphisms on Hilbert spaces
An isometry only needs to satisfy $||S(x)||=||x||$ for all $x$. It is clearly injective, but not necessarily surjective.
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