Strominger connection and pluriclosed metrics
Quanting Zhao, Fangyang Zheng
Abstract
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.
Topics & Concepts
Connection (principal bundle)Pure mathematicsMathematicsCurvatureTorsion (gastropod)Riemann curvature tensorManifold (fluid mechanics)Homogeneous spaceHermitian manifoldHermitian matrixMetric connectionConjectureMetric (unit)Mathematical analysisMathematical physicsRicci curvatureGeometryFundamental theorem of Riemannian geometryMechanical engineeringSurgeryOperations managementMedicineEconomicsEngineeringGeometry and complex manifoldsGeometric Analysis and Curvature FlowsAdvanced Algebra and Geometry