SU(3) structures on S2 bundles over four-manifolds

TL;DR

This paper constructs globally-defined SU(3) structures on certain complex manifolds, specifically on S^2 bundles over four-manifolds, extending to cases with Kähler-Einstein bases and including LT type structures.

Contribution

It provides a method to build SU(3) structures on S^2 bundles over four-dimensional complex manifolds, broadening the class of manifolds with such structures.

Findings

Successfully constructed SU(3) structures on S^2 bundles over four-manifolds.

Extended the construction to Kähler-Einstein bases with positive curvature.

Included parameter spaces that encompass LT type SU(3) structures.

Abstract

We construct globally-defined $SU(3)$ structures on smooth compact toric varieties (SCTV) in the class of $\mathbb{CP}^1$ bundles over $M$, where $M$ is an arbitrary SCTV of complex dimension two. The construction can be extended to the case where the base is K\"ahler-Einstein of positive curvature, but not necessarily toric, and admits a parameter space which includes $SU(3)$ structures of LT type.