Abstract
The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess–Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in SP( n)·SP(1), QKT connection. We study the geometry of QKT connections. We find conditions to the existence of a QKT connection and prove that if it exists it is unique. We show that QKT geometry persist in a conformal class of metrics which allows us to obtain a lot of (compact) examples of QKT manifolds. We present a (local) description of four-dimensional homogeneous QKT structures relying on the known result of naturally reductive homogeneous Riemannian manifolds. We consider Einstein-like QKT manifold and find closed relations with Einstein–Weyl geometry in dimension 4.
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