Asymptotic strictly pseudoconvex CR structure for asymptotically locally complex hyperbolic manifolds

TL;DR

This paper constructs a compactification with a strictly pseudoconvex CR structure for certain non-compact Kähler manifolds that resemble complex hyperbolic space at infinity.

Contribution

It introduces a new method to compactify asymptotically complex hyperbolic Kähler manifolds using CR structures.

Findings

Established a CR structure compactification for asymptotically complex hyperbolic manifolds

Extended the understanding of geometric structures at infinity for these manifolds

Provided tools for further analysis of their geometric and analytic properties

Abstract

In this paper, we build a compactification by a strictly pseudoconvex CR structure for complete and non-compact K\"ahler manifolds whose curvature tensor is asymptotic to that of the complex hyperbolic space.