A simple construction of generalized complex manifolds

TL;DR

This paper presents a straightforward method to construct generalized complex structures on bundles with Chern connections and homogeneous symplectic fibers, expanding known examples and enabling new holomorphic maps.

Contribution

It introduces a novel construction of generalized complex structures on bundles with specific geometric properties, extending previous work on Lie groups.

Findings

Constructs generalized complex structures on bundles with Chern connections

Provides new examples of holomorphic maps between generalized complex manifolds

Extends known constructions from Lie groups to broader settings

Abstract

We construct a natural generalized complex structure on the total space of any bundle endowed with a Chern connection and whose typical fibre is a homogeneous symplectic manifold. This extends known constructions of generalized complex structures on Lie groups and leads to natural examples of holomorphic maps between generalized complex manifolds.