CR compactification for asymptotically locally complex hyperbolic almost Hermitian manifolds

TL;DR

This paper studies complete almost Hermitian manifolds with curvature approaching that of complex hyperbolic space, showing they can be compactified with boundaries that are strictly pseudoconvex CR manifolds, revealing boundary geometry from metric expansion.

Contribution

It establishes a compactification result for asymptotically complex hyperbolic almost Hermitian manifolds and links boundary CR structures to metric asymptotics.

Findings

Manifolds can be compactified with strictly pseudoconvex CR boundary

Boundary CR structure determined by metric expansion

Provides geometric conditions for such compactifications

Abstract

In this article, we consider a complete, non-compact almost Hermitian manifold whose curvature is asymptotic to that of the complex hyperbolic plane. Under natural geometric conditions, we show that such a manifold arises as the interior of a compact almost complex manifold whose boundary is a strictly pseudoconvex CR manifold. Moreover, the geometric structure of the boundary can be recovered by analysing the expansion of the metric near infinity.