Pluriclosed manifolds with parallel Bismut torsion

TL;DR

This paper classifies simply-connected pluriclosed manifolds with parallel Bismut torsion and proves a splitting theorem for compact Calabi-Yau with torsion manifolds that are also pluriclosed with this property.

Contribution

It extends existing classifications and introduces a splitting theorem for a specific class of manifolds with special geometric structures.

Findings

Complete classification of simply-connected pluriclosed manifolds with parallel Bismut torsion.

Splitting theorem for compact Calabi-Yau with torsion and pluriclosed with parallel Bismut torsion.

Extension of known results in complex and differential geometry.

Abstract

We present a complete classification of simply-connected pluriclosed manifolds with parallel Bismut torsion, extending previously known results in the literature. Consequently, we also establish a splitting theorem for compact manifolds that are both pluriclosed with parallel Bismut torsion and Calabi-Yau with torsion.