Calibrations in hyperkahler geometry

Details Calibrations in hyperkahler geometry Calibrations in hyperkahler geometry

2010-09-06

arxiv.org/abs/1009.1178v3

Mathematics

Differential Geometry

v. 2.0, 32 pages, reference added, some examples, minor misprints etc

Scientific paper

We describe a family of calibrations arising naturally on a hyperk\"ahler manifold $M$. These calibrations calibrate the holomorphic Lagrangian, holomorphic isotropic and holomorphic coisotropic subvarieties. When $M$ is an HKT (hyperkaehler with torsion) manifold with holonomy $SL(n, {\Bbb H})$, we construct another family of calibrations $\Phi_i$, which calibrates holomorphic Lagrangian and holomorphic coisotropic subvarieties. The calibrations $\Phi_i$ are (generally speaking) not parallel with respect to any torsion-free connection on $M$.

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