Harmonic metrics and semi-simpleness
Differential Geometry
2023-04-24 v1
Abstract
Given a flat vector bundle over a compact Riemannian manifold, Corlette and Donaldson proved that it admits harmonic metrics if and only if it is semi-simple. In this paper, we extend this equivalence to arbitrary vector bundles without any additional hypothesis, the result can be viewed as a Riemannian Hitchin-Kobayashi correspondence. Furthermore, we also prove an equivalence of categories in Sasakian geometry, relating the category of projective flat complex vector bundles to the category of Higgs bundles.
Cite
@article{arxiv.2304.10800,
title = {Harmonic metrics and semi-simpleness},
author = {Di Wu and Xi Zhang},
journal= {arXiv preprint arXiv:2304.10800},
year = {2023}
}