Rotational conformal transformations of the Lobachevskij plane (Q1603097)

In a two-dimensional Riemannian space of non-zero Gaussian curvature a curve whose geodesic curvature is proportional to the Gaussian curvature is an isoperimetric rotational extremal (IRE). A transformation of a region of the space which sends geodesic curves of IRE's is said to be rotational. The authors prove that the group of rotational conformal transformations of the Lobachevskij plane coincides with the Möbius group of conformal transformations of this plane.