Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry

被引：41

作者：

Alesker, Semyon ^{[1
]}

Verbitsky, Misha

机构：

[1] Tel Aviv Univ, Dept Math, IL-69978 Tel Aviv, Israel

[2] Univ Glasgow, Dept Math, Glasgow G12 8QW, Lanark, Scotland

[3] Inst Theoret & Expt Phys, Moscow 117259, Russia

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2006年 / 16卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

plurisubharmonic functions; hypercomplex manifolds; quaternions; HKT-metric;

D O I：

10.1007/BF02922058

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 (hyperkahler with torsion) metrics. We prove a quaternionic analogue of A. D. Aleksandrov and Chem-Levine-Nirenberg theorems.

引用

页码：375 / 399

页数：25

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