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Geometry of Quaternionic K\"ahler connections with torsion

Stefan Ivanov
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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. Studying conformal transformations we obtain a lot of (compact) examples of QKT manifolds. We present a (local) description of 4-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 four.

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Stefan Ivanov. 2000-03-30. Geometry of Quaternionic K\"ahler connections with torsion. https://doi.org/10.1016/s0393-0440(01)00058-4

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