On balanced Hermitian threefolds with parallel Bismut torsion

TL;DR

This paper characterizes all compact, balanced Bismut torsion parallel (BTP) threefolds, expanding understanding of non-Kähler Hermitian manifolds with parallel Bismut torsion.

Contribution

It provides a detailed classification of all compact, balanced BTP threefolds, a significant step in understanding their geometric structure.

Findings

Complete characterization of compact balanced BTP threefolds

Identification of conditions for non-Kähler BTP metrics

Advancement in the study of Hermitian manifolds with parallel Bismut torsion

Abstract

We continue our study on Hermitian manifolds that are {\em Bismut torsion parallel,} or {\em BTP} for brevity, which means that the Bismut connection has parallel torsion tensor. For $n\geq 3$, BTP metrics can be balanced (and non-K\"ahler). In this paper, we give a detailed description to characterize all compact, balanced BTP threefolds.