Abstract:
We describe a family of calibrations arising naturally on a hyperkaehler manifold $M$. These calibrationscalibrate the holomorphic Lagrangian, holomorphic isotropic and holomorphic coisotropic subvarieties. When $M$ is an HKT (hyperkahler with torsion) manifold with holonomy $SL(n,H)$, we construct another family of calibrations, which calibrate holomorphic Lagrangian and holomorphic coisotropic subvarieties. They are (generally speaking) not parallel with respect to any torsionless connection on $M$. We note also that there are examples of complex isotropic submanifolds in $SL(n,H)$ manifolds with HKT structure, which can not be calibrated by any form, unlike the Kaehler case.
