Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry
Abstract
A hypercomplex manifold is a manifold equipped with a triple of complex structures
I,J,K
satisfying the quaternionic relations. We define a quaternionic analogue of plurisubharmonic functions on hypercomplex manifolds, and interpret these functions geometrically as potentials of HKT (hyperkähler with torsion) metrics, and prove a quaternionic analogue of A.D. Aleksandrov and Chern-Levine-Nirenberg theorems.