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Geometric structures on complex manifolds
October 3, 2011 15:00, Moscow
 


Calibrations in hyperkaehler geometry

Gueo Grantcharov

Florida International University
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Gueo Grantcharov


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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.

Language: English

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