On Hermitian manifolds with Bismut-Strominger parallel torsion

TL;DR

This paper characterizes Hermitian manifolds with Bismut-Strominger connection having parallel torsion, providing classification results for various subclasses including threefolds, thus advancing understanding of their geometric structure.

Contribution

It offers a necessary and sufficient curvature condition for BTP manifolds and classifies non-balanced and balanced BTP threefolds, extending previous results.

Findings

BTP manifolds include Bismut flat and Bismut Kähler-like manifolds

Structural results for non-balanced BTP manifolds

Classification theorems for BTP threefolds

Abstract

In this article, we study Hermitian manifolds whose Bismut-Strominger connection has parallel torsion tensor, which will be called {\em Bismut torsion parallel manifolds,} or {\em BTP} manifolds for short. We obtain a necessary and sufficient condition characterizing this class in terms of the curvature tensor. In particular, Bismut flat or Bismut K\"ahler-like manifolds are {\em BTP} manifolds, known by our earlier results. We also obtain structural results for non-balanced {\em BTP} manifolds, and classification theorems for non-balanced {\em BTP} threefolds and balanced {\em BTP} threefolds.