Sasakian and parabolic Higgs bundles

TL;DR

This paper establishes a correspondence between Sasakian G-Higgs bundles on certain manifolds and parabolic G-Higgs bundles on their base varieties, linking geometric structures across different settings.

Contribution

It introduces an equivalence between Sasakian G-Higgs bundles and parabolic G-Higgs bundles, expanding the understanding of Higgs bundle classifications on complex manifolds.

Findings

Established an equivalence between Sasakian and parabolic Higgs bundles.

Connected geometric structures on Sasakian manifolds with parabolic bundles on projective varieties.

Provides a new framework for studying Higgs bundles in complex geometry.

Abstract

Let $M$ be a quasi-regular compact connected Sasakian manifold, and let $N = M/S^1$ be the base projective variety. We establish an equivalence between the class of Sasakian $G$-Higgs bundles over $M$ and the class of parabolic (or equivalently, ramified) $G$-Higgs bundles over the base $N$.