On the Canonical Cusps in Complex Hyperbolic Surfaces

Abstract

Abstract. In this paper, we consider the canonical cusps in complex hyperbolic surfaces. We will classify canonical cusps in complex hyperbolic surfaces and find correspondence between them and 3-dimensional nilpotent groups. This paper is a sequel of our paper [6].

Two-generator groups acting on the complex hyperbolic plane

“…See also [63] where the bounds on volumes of cusps obtained in [50,77] and [77] are improved, and [51] where the author uses arguments from algebraic geometry. The specific case of H 2 C is also studied in [65]. For generalisations to the frame of quaternionic hyperbolic geometry, see [62,64].…”

“…C is also studied in [65]. For generalisations to the frame of quaternionic hyperbolic geometry, see [62,64].…”