Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry
Complex Variables
2017-11-03 v4 Differential Geometry
Abstract
A hypercomplex manifold is a manifold equipped with a triple of complex structures 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.
Cite
@article{arxiv.math/0510140,
title = {Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry},
author = {Semyon Alesker and Misha Verbitsky},
journal= {arXiv preprint arXiv:math/0510140},
year = {2017}
}
Comments
34 pages. Minor corrections