The complex hyperbolic Kleinian groups with an invariant totally geodesic submanifold

TL;DR

This paper characterizes certain discrete subgroups of PU(2,1) that preserve a totally geodesic submanifold in complex hyperbolic space, enhancing understanding of their geometric and algebraic properties.

Contribution

It provides a characterization of complex hyperbolic Kleinian groups with invariant totally geodesic submanifolds, a novel classification in complex hyperbolic geometry.

Findings

Identification of conditions for invariance of totally geodesic submanifolds

Classification of discrete subgroups with invariant submanifolds

Insights into the structure of complex hyperbolic Kleinian groups

Abstract

In this notes, we characterize discrete subgroups of PU(2,1), holomorphic isometric group of complex hyperbolic space, which have an invariant totally geodesic submanifold.