Geometry of quaternionic Kahler connections with torsion

JOURNAL OF GEOMETRY AND PHYSICS

卷:41

Article

Ivanov, S

关键词: almost quaternionic;    hyper Hermitian;    quaternionic Kahler;    torsion;    locally conformal quatentionic Kahler;    naturally reductive homogeneous Riemannian;    spaces;    Einstein-Weyl geometry;   

DOI  :  10.1016/S0393-0440(01)00058-4

来源: Elsevier

【 摘 要 】

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. (C) 2002 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free