2000/03/30 by Stefan Ivanov · 37 citations
Mathematics · Physics and Astronomy · #Affine connection #Black Holes and Theoretical Physics #Combinatorics #Conformal geometry #Conformal map #Conformal symmetry #Connection (principal bundle) #Curvature #Differential geometry #Einstein #Fundamental theorem of Riemannian geometry #Geodesic #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Holonomy #Homogeneous #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Metric connection #Pure mathematics #Scalar curvature #Torsion (gastropod) #math.DG #msc:32L25 #msc:53C15 #msc:53C25 #msc:53C56 #msc:57S25
paper · pdf · doi:10.1016/s0393-0440(01)00058-4
published in Journal of Geometry and Physics 41(3), 235-257 (Elsevier BV) · LaTeX, 21 pages
arxiv created 2000/03/30 · openalex publication_date 2002/03/01 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.