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Article

Quaternionic Monge-Ampere equation and Calabi problem for HKT-manifolds

Israel Journal of Mathematics. 2010. Vol. 176. No. 1. P. 109-138.
Alesker S., Verbitsky M.
We describe a family of calibrations arising naturally on a hyperk¨ahler manifoldM. These calibrations calibrate the holomorphic Lagrangian, holomorphic isotropic and holomorphic coisotropic subvarieties. When M is an HKT (hyperk¨ahler with torsion) manifold with holonomy SL(n,H), we construct another family of calibrations i, which calibrates holomorphic Lagrangian and holomorphic coisotropic subvarieties. The calibrations i are (generally speaking) not parallel with respect to any torsion-free connection on M.