Strominger connection and pluriclosed metrics

Authors：Zhao, Quanting; Zheng, Fangyang^*

Source：Journal für die Reine und Angewandte Mathematik, 2023, 2023(796): 245-267.

DOI：10.1515/crelle-2023-0007

• VANISHING THEOREMS
• LIE-GROUPS
• KAHLER
• MANIFOLDS
• EXISTENCE
• TORSION

In this paper, we prove a conjecture raised by Angella, Otal, Ugarte and Villacampa recently, which states that if the Strominger connection (also known as Bismut connection) of a compact Hermitian manifold is Kahler-like, in the sense that its curvature tensor obeys all the symmetries of the curvature of a Kahler manifold, then the metric must be pluriclosed. What we actually showed is a bit more: for any given Hermitian manifold, the Strominger Kahler-like condition is equivalent to the pluriclosedness of the metric plus the parallelness of the torsion.

• Institution
  重庆师范大学