Reduction of metric structures on Courant algebroids

TL;DR

This paper develops a reduction procedure for metric structures on Courant algebroids, enabling the derivation of known results and new insights, such as the structure of moduli spaces of instantons on special manifolds.

Contribution

It introduces a novel reduction method for strong KT, hyper KT, and generalized Kähler structures on Courant algebroids, providing a new perspective on their properties.

Findings

Recovered existing results on metric structures via reduction

Showed moduli spaces of instantons inherit similar structures

Provided a new geometric interpretation of these structures

Abstract

We use the procedure of reduction of Courant algebroids to reduce strong KT, hyper KT and generalized Kaehler structures on Courant algebroids. This allows us to recover results from the literature as well as explain from a different angle some of the features observed there in. As an example, we prove that the moduli space of instantons of a bundle over a SKT/HKT/generalized K\"ahler manifold is endowed with the same type of structure as the original manifold.