Plurisubharmonic functions on hypercomplex manifolds and HKT- geometry

Alesker, S. and Verbitski, M. (2006) Plurisubharmonic functions on hypercomplex manifolds and HKT- geometry. Journal of Geometric Analysis, 16(3), pp. 375-399. (doi:10.1007/BF02922058)

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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. We prove a quaternionic analogue of A. D. Aleksandrov and ChernLevine-Nirenberg theorems.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Verbitski, Dr Mikhail
Authors: Alesker, S., and Verbitski, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Geometric Analysis
Journal Abbr.:J. Geom. Anal.
ISSN:1050-6926
ISSN (Online):1559-002X
Published Online:29 June 2008

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
316541Hyperkaehler manifoldsMikhail VerbitskiEngineering & Physical Sciences Research Council (EPSRC)GR/R77773/01Mathematics