Hypercomplex limits of pluricomplex structures and the Euclidean limit of hyperbolic monopoles

TL;DR

This paper explores the geometric transition from hyperbolic monopoles to Euclidean monopoles using pluricomplex geometry, and studies the limits of hypercomplex manifolds derived from pluricomplex structures.

Contribution

It introduces a geometric framework for understanding the Euclidean limit of hyperbolic monopoles through hypercomplex and pluricomplex geometry.

Findings

Characterization of Euclidean limits of hyperbolic monopoles

Analysis of hypercomplex manifolds as limits of pluricomplex structures

Insights into the geometric structures underlying monopole limits

Abstract

We discuss the Euclidean limit of hyperbolic SU(2)-monopoles, framed at infinity, from the point of view of pluricomplex geometry. More generally, we discuss the geometry of hypercomplex manifolds arising as limits of pluricomplex manifolds.