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- Title
HKT Manifolds with Holonomy SL(n,H).
- Authors
Ivanov, Stefan; Petkov, Alexander
- Abstract
We show that on an hyper-Kähler with torsion (HKT) manifold the holonomy of the Obata connection is contained in if and only if the Lee form is an exact 1-form. As an application, we show compact HKT manifolds with holomorphically trivial canonical bundle that are not balanced. A simple criterion for nonexistence of HKT metric on hypercomplex manifold is given in terms of the Ricci-type tensors of the Obata connection.
- Subjects
MANIFOLDS (Mathematics); HOLONOMY groups; KAHLERIAN manifolds; TORSION theory (Algebra); MATHEMATICAL forms; HOLOMORPHIC functions
- Publication
IMRN: International Mathematics Research Notices, 2012, Vol 2012, Issue 16, p3779
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnr160