Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry

Details Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry

2005-10-07

arxiv.org/abs/math/0510140v2

J. Geom. Anal. 16 (2006), no. 3, 375--399.

Mathematics

Complex Variables

34 pages; revised version; a proposition is added to Section 8; appropriate modifications in the introduction

Scientific paper

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 (hyperk\"ahler with torsion) metrics, and prove a quaternionic analogue of A.D. Aleksandrov and Chern-Levine-Nirenberg theorems.

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