Abstract
Lie groups of bi-Mobius transformations are known and their actions on non orientable n-dimensional complex manifolds have been studied. In this paper, m-Mobius transformations are introduced and similar problems as those related to bi-Mobius transformations are tackled. In particular, it is shown that the subgroup generated by every m-Mobius transformation is a discrete group. Cyclic subgroups are exhibited. Vector valued m-Mobius transformations are also studied.
Highlights
When investigating Lie groups of Möbius transformations of the Riemann sphere, we were brought in [1] [2] and [3] to the study of some bi-Möbius transformations
M-Möbius transformations are introduced and similar problems as those related to bi-Möbius transformations are tackled
It is shown that the subgroup generated by every m-Möbius transformation is a discrete group
Summary
When investigating Lie groups of Möbius transformations of the Riemann sphere, we were brought in [1] [2] and [3] to the study of some bi-Möbius transformations. These are functions f : × → of the form: f ( z1, z2 ). An easy computation shows that for fixed ω1 and ω2 the equations f1 ( z1, z2 ) = b1 and f2 ( z1, z2 ) = b2 determine uniquily z1 + z2 and z1z2 belonging to 2 σ We can call this mapping Möbius transformation of 2 σ. The study of these mappings is worthwhile, yet it exceeds the purpose of this note
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