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Hypercomplex structures on Kähler manifolds

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Geometric & Functional Analysis GAFA Aims and scope Submit manuscript

Abstract.

Let (M, I) be a compact Kähler manifold admitting a hypercomplex structure (M, I, J, K). We show that (M, I, J, K) admits a natural HKT-metric. This is used to construct a holomorphic symplectic form on (M, I).

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Authors and Affiliations

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

    M. Verbitsky

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

    M. Verbitsky

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  1. M. Verbitsky
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Correspondence to M. Verbitsky.

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Received: August 2004 Revision: August 2004 Accepted: August 2004

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Verbitsky, M. Hypercomplex structures on Kähler manifolds. GAFA, Geom. funct. anal. 15, 1275–1283 (2005). https://doi.org/10.1007/s00039-005-0537-4

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  • DOI: https://doi.org/10.1007/s00039-005-0537-4

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