Notes on complex hyperbolic triangle groups of type (m,n,infinity)

TL;DR

This paper investigates the properties and conditions for discreteness of complex hyperbolic triangle groups of type (m, n, infinity), providing insights into their structure and specific cases like (n, infinity, infinity).

Contribution

It offers new criteria and analysis for the discreteness of complex hyperbolic triangle groups of certain types, expanding understanding of their geometric properties.

Findings

Discreteness conditions for (m, n, infinity) groups derived.

Explicit conclusions for (n, infinity, infinity) groups provided.

Enhanced understanding of complex hyperbolic triangle group structures.

Abstract

In this paper we mainly pay attention to the complex hyperbolic triangle groups of type (m, n, infinity) and discuss the discreteness. From the results more explicit conclusions about the triangle groups of type (n, infinity, infinity) will also be given.