Calabi-Yau Connections with Torsion on Toric Bundles

TL;DR

This paper establishes conditions under which certain toric bundles over Kähler manifolds admit Calabi-Yau connections with torsion, and constructs explicit examples using topological classification.

Contribution

It provides new criteria for Calabi-Yau connections with torsion on toric bundles and constructs explicit geometric examples on specific topological manifolds.

Findings

Sufficient conditions for existence of Calabi-Yau connections with torsion

Construction of such geometries on connected sums of sphere products

Topological classification aids in explicit example construction

Abstract

We find sufficient conditions for a principal toric bundle over compact K\"ahler manifolds to admit Calabi-Yau connections with torsion. With the aids of a topological classification, we construct such geometry on $n(S^2\times S^4)#(n+1)(S^3\times S^3)$