Bogomolny equations and conformal transformations in curved space

TL;DR

This paper explores how Bogomolny equations can be derived and generalized in curved space using conformal transformations, extending previous results and coupling the Higgs field with the Ricci tensor.

Contribution

It introduces a method to derive Bogomolny equations in curved space via conformal rescaling, generalizing to any static background metric.

Findings

Recovered earlier results on Bogomolny equations in curved space

Derived coupling of Higgs field with Ricci tensor using conformal rescaling

Generalized the procedure to any static background metric

Abstract

The coupling of the Higgs field through the Ricci tensor, put forward by Balakrishna and Wali, is derived using a conformal rescaling of the metric. Earlier results on "Bogomolny-type" equations in curved space, by Comtet, and others, are recovered. The procedure can be generalized to any static background metric.