THE QUATERNIONIC/HYPERCOMPLEX-CORRESPONDENCE

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Abstract

Given a quaternionic manifold M with a certain U(1)-symmetry, we construct a hypercomplex manifold M' of the same dimension. This construction generalizes the quaternionic Kähler/ hyper-Kähler-correspondence. As an example of this construction, we obtain a compact homogeneous hypercomplex manifold which does not admit any hyper-Kähler structure. Therefore our construction is a proper generalization of the quaternionic Kähler/hyper-Kähler-correspondence.

Journal

  • Osaka Journal of Mathematics

    Osaka Journal of Mathematics 58 (1), 213-238, 2021-01

    Osaka University and Osaka City University, Departments of Mathematics

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