| Autor: |
Soldatenkov, Andrey, Verbitsky, Misha |
| Předmět: |
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| Zdroj: |
IMRN: International Mathematics Research Notices; 2015, Vol. 2015 Issue 4, p981-994, 11p |
| Abstrakt: |
A hypercomplex manifold is amanifold equipped with a triple of complex structures satisfying the quaternionic relations. A holomorphic Lagrangian variety on a hypercomplex manifold with trivial canonical bundle is a holomorphic subvariety which is calibrated by a form associated with the holomorphic volume form; this notion is a generalization of the usual holomorphic Lagrangian subvarieties known in hyperKähler geometry. An HKT (hyperKähler with torsion) metric on a hypercomplex manifold is a metric determined by a local potential, in a similar way to the Kähler metric. We prove that a base of a holomorphic Lagrangian fibration is always Kähler, if its total space is HKT. This is used to construct new examples of hypercomplex manifolds which do not admit an HKT structure. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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