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Extremal metrics in quaternionic geometry
Кстати, слайды с моей

лекции во вторник
http://verbit.ru/MATH/TALKS/CY-HKT-CIRM.pdf

A hypercomplex manifold is a manifold equipped with three
complex structure I, J, K, satisfying quaternionic
relations. A quaternionic Hermitian metric is called HKT
if it is locally given by a quaternionic plurisubharmonic
potential in a similar way to Kaehler metrics defined from
plurisubharmonic potentials. I will define the
quaternionic Monge-Ampere equation and explain how it
can be used to characterize the extremal HKT metrics
on hypercomplex manifolds. I will prove their
uniqueness on hypercomplex manifolds with trivial
and negative canonical bundle.

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