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Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry

Semyon Alesker·Misha Verbitsky
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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.

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Semyon Alesker, Misha Verbitsky. 2017-11-02. Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry. https://arxiv.org/abs/math/0510140

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