Strominger connection and pluriclosed metrics

Abstract

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 Kähler-like, in the sense that its curvature tensor obeys all the symmetries of the curvature of a Kähler manifold, then the metric must be pluriclosed. What we actually showed is a bit more: for any given Hermitian manifold, the Strominger Kähler-like condition is equivalent to the pluriclosedness of the metric plus the parallelness of the torsion.

References in corpus (1)

• On Gauduchon connections with Kähler-like curvature

Cited by in corpus (6)

• On Gauduchon connections with Kähler-like curvature
• Deformed Hermitian-Yang-Mills Equation on Compact Hermitian Manifolds
• Complex nilmanifolds and Kähler-like connections
• Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics
• Curvatures of real connections on Hermitian manifolds
• A new positivity condition for the curvature of Hermitian manifolds