A Construction of Non-K\"ahler Calabi-Yau Manifolds and New Solutions to the Strominger System

TL;DR

This paper introduces a novel method to construct compact non-K"ahler Calabi-Yau manifolds with balanced metrics and provides explicit solutions to the Strominger system on these manifolds, including cases with degeneracies.

Contribution

It presents a new construction of non-K"ahler Calabi-Yau manifolds and explicitly solves the Strominger system on them, expanding understanding of these complex geometries.

Findings

Constructed non-K"ahler Calabi-Yau manifolds with balanced metrics.

Obtained explicit solutions to the Strominger system with degeneracies.

Analyzed solutions on manifolds involving minimal surfaces in tori.

Abstract

We propose a new construction of compact non-K\"ahler Calabi-Yau manifolds with balanced metrics and study the Strominger system on them. In particular, we obtain explicit solutions to the Strominger system with degeneracies on $\Sigma_g\times T^4$, where $\Sigma_g$ is an immersed minimal surface of genus $g\geq3$ in $T^3$.