Kleinian orbifolds uniformized by RP groups with an elliptic and a hyperbolic generator

TL;DR

This paper studies a special class of Kleinian groups generated by an elliptic and a hyperbolic element, providing their presentations and classifying the orbifolds they uniformize.

Contribution

It offers a complete classification and presentation of orbifolds uniformized by Kleinian groups generated by an elliptic and a hyperbolic element with axes in one plane.

Findings

Presentations of such Kleinian groups

Complete list of uniformized orbifolds

Classification of orbifolds based on group generators

Abstract

We consider non-elementary Kleinian groups \Gamma, without invariant plane, generated by an elliptic and a hyperbolic element with their axes lying in one plane. We find presentations and a complete list of orbifolds uniformized by such \Gamma.