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Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry |
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| Authors: | Semyon Alesker Misha Verbitsky |
| Affiliation: | 1. Department of Mathematics, Tel Aviv University, 69978, Ramat Aviv, Tel Aviv, Israel 2. Department of Mathematics, University of Glasgow, 15 University Gardens, G12 8QW, Glasgow, Scotland 3. Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya, 25, 117259, Moscow, Russia |
| 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. |
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