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Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry

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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.

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Authors and Affiliations

  1. Department of Mathematics, Tel Aviv University, 69978, Ramat Aviv, Tel Aviv, Israel

    Semyon Alesker & Misha Verbitsky

  2. Department of Mathematics, University of Glasgow, 15 University Gardens, G12 8QW, Glasgow, Scotland

    Semyon Alesker & Misha Verbitsky

  3. Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya, 25, 117259, Moscow, Russia

    Semyon Alesker & Misha Verbitsky

Authors
  1. Semyon Alesker
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  2. Misha Verbitsky
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Communicated by Gennadi M. Henkin

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Alesker, S., Verbitsky, M. Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry. J Geom Anal 16, 375–399 (2006). https://doi.org/10.1007/BF02922058

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  • DOI: https://doi.org/10.1007/BF02922058

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