Abstract
AbstractIn both the Euclidean plane $${\mathbb {R}}^2$$
R
2
and the hyperbolic plane $${\mathbb {H}}^2$$
H
2
, a non-trivial group of rotations has a unique fixed point. We compare groups of rotations of the three-dimensional spaces $${\mathbb {R}}^3$$
R
3
and $${\mathbb {H}}^3$$
H
3
, and in each case we discuss the existence of a (possibly non-unique) common fixed point of the elements in such a group.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Analysis
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