HKT manifolds with holonomy SL(n,H)

Details HKT manifolds with holonomy SL(n,H) HKT manifolds with holonomy SL(n,H)

2010-10-25

arxiv.org/abs/1010.5052v4

Mathematics

Differential Geometry

14 pages, LaTeX2e, exposition in section 5 clarified, final version, to appear in Int. Math. Res. Notices (IMRN)

Scientific paper

We show that on an HKT manifold the holonomy of the Obata connection is contained in SL(n,H) if and only if the Lee form is an exact one form. As an application, we show compact HKT manifolds with holomorphically trivial canonical bundle which are not balanced. A simple criterion for non-existence of HKT metric on hypercomplex manifold is given in terms of the Ricci-type tensors of the Obata connection.

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