Geometry of quaternionic Kähler connections with torsion

✍ Scribed by Stefan Ivanov

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 141 KB
• Volume: 41
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(01)00058-4

✦ Synopsis

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.